| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$2$ |
$3$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$68.79260$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$7.334270539$ |
0.771683 |
\( 24164258357939329603 a^{5} - 32090567672134595043 a^{4} - 110295011211469229354 a^{3} + 132835771594028505313 a^{2} + 77248781181165510499 a - 73667499983669418847 \) |
\( \bigl[a^{4} - 4 a^{2} + a + 2\) , \( -a^{5} + a^{4} + 4 a^{3} - 5 a^{2} - 2 a + 4\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 2\) , \( 13 a^{5} - 17 a^{4} - 56 a^{3} + 73 a^{2} + 34 a - 48\) , \( 69 a^{5} - 97 a^{4} - 310 a^{3} + 403 a^{2} + 206 a - 237\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+2\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-5a^{2}-2a+4\right){x}^{2}+\left(13a^{5}-17a^{4}-56a^{3}+73a^{2}+34a-48\right){x}+69a^{5}-97a^{4}-310a^{3}+403a^{2}+206a-237$ |
| 1.1-a2 |
1.1-a |
$2$ |
$3$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$68.79260$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$5346.683223$ |
0.771683 |
\( 1285592 a^{5} - 1709472 a^{4} - 5867135 a^{3} + 7077626 a^{2} + 4106851 a - 3927865 \) |
\( \bigl[a^{4} - 4 a^{2} + a + 2\) , \( -a^{5} + a^{4} + 4 a^{3} - 5 a^{2} - 2 a + 4\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 2\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 12 a^{2} - 6 a + 7\) , \( 0\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+2\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-5a^{2}-2a+4\right){x}^{2}+\left(-2a^{5}+3a^{4}+9a^{3}-12a^{2}-6a+7\right){x}$ |
| 7.1-a1 |
7.1-a |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{10} \) |
$80.90336$ |
$(a^4-4a^2+a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1353.901052$ |
0.879334 |
\( -\frac{6378555847697446312}{282475249} a^{5} - \frac{2474411833285999287}{282475249} a^{4} + \frac{28471855515534194816}{282475249} a^{3} + \frac{13996124332632398039}{282475249} a^{2} - \frac{12521297730192365783}{282475249} a - \frac{4603543349670581566}{282475249} \) |
\( \bigl[a^{4} - 3 a^{2} + a - 1\) , \( -a^{5} + a^{4} + 4 a^{3} - 5 a^{2} - a + 5\) , \( a\) , \( -8 a^{5} + 11 a^{4} + 31 a^{3} - 43 a^{2} - 9 a + 9\) , \( -21 a^{5} + 25 a^{4} + 63 a^{3} - 113 a^{2} + 14 a + 21\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-5a^{2}-a+5\right){x}^{2}+\left(-8a^{5}+11a^{4}+31a^{3}-43a^{2}-9a+9\right){x}-21a^{5}+25a^{4}+63a^{3}-113a^{2}+14a+21$ |
| 7.1-a2 |
7.1-a |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{5} \) |
$80.90336$ |
$(a^4-4a^2+a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2707.802104$ |
0.879334 |
\( \frac{1519176145}{16807} a^{5} + \frac{970371936}{16807} a^{4} - \frac{5971587107}{16807} a^{3} - \frac{3315408956}{16807} a^{2} + \frac{2656017515}{16807} a + \frac{1004044424}{16807} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 2\) , \( a^{4} - 4 a^{2} + a + 1\) , \( 2 a^{4} - 2 a^{3} - 7 a^{2} + 4 a + 2\) , \( a^{4} - 5 a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(2a^{4}-2a^{3}-7a^{2}+4a+2\right){x}+a^{4}-5a^{2}+a+1$ |
| 13.1-a1 |
13.1-a |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{5} \) |
$85.18641$ |
$(-a^3+3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.000371934$ |
$131140.2253$ |
1.90073 |
\( -\frac{103100163311}{371293} a^{5} + \frac{182729681141}{371293} a^{4} + \frac{362887267482}{371293} a^{3} - \frac{683775071524}{371293} a^{2} + \frac{70645965670}{371293} a + \frac{102890932488}{371293} \) |
\( \bigl[a^{5} - 4 a^{3} + 2 a\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + a\) , \( a^{2} + a - 1\) , \( -2 a^{4} - a^{3} + 6 a^{2} - 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+2a\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+a\right){x}^{2}+\left(-2a^{4}-a^{3}+6a^{2}-2\right){x}$ |
| 31.1-a1 |
31.1-a |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$91.58448$ |
$(-a^5+5a^3-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$494.6028815$ |
1.28494 |
\( -\frac{14206653307178619495}{961} a^{5} - \frac{5497977302510641703}{961} a^{4} + \frac{63407570964288615284}{961} a^{3} + \frac{31119698730479344528}{961} a^{2} - \frac{899039953178525727}{31} a - \frac{10242719039868077233}{961} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( a^{5} - 5 a^{3} + a^{2} + 3 a - 3\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( 17 a^{5} - 24 a^{4} - 67 a^{3} + 89 a^{2} + 21 a - 30\) , \( -32 a^{5} + 64 a^{4} + 107 a^{3} - 253 a^{2} + 71 a + 24\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-3\right){y}={x}^{3}+\left(a^{5}-5a^{3}+a^{2}+3a-3\right){x}^{2}+\left(17a^{5}-24a^{4}-67a^{3}+89a^{2}+21a-30\right){x}-32a^{5}+64a^{4}+107a^{3}-253a^{2}+71a+24$ |
| 31.1-a2 |
31.1-a |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$91.58448$ |
$(-a^5+5a^3-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3956.823052$ |
1.28494 |
\( \frac{1524420667}{31} a^{5} + \frac{589876778}{31} a^{4} - \frac{6803520577}{31} a^{3} - \frac{3338194444}{31} a^{2} + 96463426 a + \frac{1098598601}{31} \) |
\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 5 a - 2\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 6 a - 7\) , \( a^{5} - 4 a^{3} + 2 a - 1\) , \( -3 a^{5} - a^{4} + 20 a^{3} - 5 a^{2} - 15 a + 3\) , \( -3 a^{5} + 5 a^{4} + a^{3} + 3 a^{2} - 6\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-9a^{3}+4a^{2}+5a-2\right){x}{y}+\left(a^{5}-4a^{3}+2a-1\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+6a-7\right){x}^{2}+\left(-3a^{5}-a^{4}+20a^{3}-5a^{2}-15a+3\right){x}-3a^{5}+5a^{4}+a^{3}+3a^{2}-6$ |
| 31.1-b1 |
31.1-b |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$91.58448$ |
$(-a^5+5a^3-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5001.214246$ |
1.62410 |
\( \frac{2995464392}{31} a^{5} + \frac{1293428394}{31} a^{4} - \frac{8899729189}{31} a^{3} + \frac{17678994}{31} a^{2} + 72760745 a + \frac{420249726}{31} \) |
\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 6 a - 5\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 12 a^{2} + 6 a - 4\) , \( a^{4} - 4 a^{2} + 1\) , \( -a^{5} + 7 a^{3} - a^{2} - 5 a + 4\) , \( 4 a^{5} - 4 a^{4} - 18 a^{3} + 19 a^{2} + 12 a - 10\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-9a^{3}+5a^{2}+6a-5\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-9a^{3}+12a^{2}+6a-4\right){x}^{2}+\left(-a^{5}+7a^{3}-a^{2}-5a+4\right){x}+4a^{5}-4a^{4}-18a^{3}+19a^{2}+12a-10$ |
| 31.1-b2 |
31.1-b |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{2} \) |
$91.58448$ |
$(-a^5+5a^3-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2500.607123$ |
1.62410 |
\( \frac{139573028727470950776}{961} a^{5} + \frac{146091909064081505603}{961} a^{4} - \frac{398857975268896914941}{961} a^{3} - \frac{258052846331700559100}{961} a^{2} + \frac{5474415068525499730}{31} a + \frac{68193984513407074549}{961} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 9 a^{2} - 5 a + 6\) , \( a^{5} - 4 a^{3} + a - 1\) , \( -18 a^{5} + 35 a^{4} + 48 a^{3} - 86 a^{2} - 25 a + 31\) , \( -51 a^{5} + 152 a^{4} - 32 a^{3} - 169 a^{2} + 64 a + 14\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-4\right){x}{y}+\left(a^{5}-4a^{3}+a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-9a^{2}-5a+6\right){x}^{2}+\left(-18a^{5}+35a^{4}+48a^{3}-86a^{2}-25a+31\right){x}-51a^{5}+152a^{4}-32a^{3}-169a^{2}+64a+14$ |
| 31.1-c1 |
31.1-c |
$4$ |
$4$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$91.58448$ |
$(-a^5+5a^3-5a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12318.19278$ |
1.00006 |
\( -\frac{526618}{31} a^{5} + \frac{9219416}{31} a^{4} + \frac{18276705}{31} a^{3} - \frac{15857144}{31} a^{2} - 975716 a - \frac{7676519}{31} \) |
\( \bigl[a^{2} - 2\) , \( a^{5} - 5 a^{3} - a^{2} + 3 a + 1\) , \( a^{2} + a - 2\) , \( -4 a^{5} + a^{4} + 19 a^{3} - 2 a^{2} - 14 a - 2\) , \( -6 a^{5} + 6 a^{4} + 29 a^{3} - 23 a^{2} - 26 a + 6\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{5}-5a^{3}-a^{2}+3a+1\right){x}^{2}+\left(-4a^{5}+a^{4}+19a^{3}-2a^{2}-14a-2\right){x}-6a^{5}+6a^{4}+29a^{3}-23a^{2}-26a+6$ |
| 31.1-c2 |
31.1-c |
$4$ |
$4$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$91.58448$ |
$(-a^5+5a^3-5a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$1539.774098$ |
1.00006 |
\( \frac{1264802592419037}{961} a^{5} + \frac{1051692343665191}{961} a^{4} - \frac{4077796430304573}{961} a^{3} - \frac{1864472573084891}{961} a^{2} + \frac{75867838088346}{31} a + \frac{820784281275104}{961} \) |
\( \bigl[a^{2} - 2\) , \( a^{5} - 5 a^{3} - a^{2} + 3 a + 1\) , \( a^{2} + a - 2\) , \( -14 a^{5} - 14 a^{4} + 84 a^{3} + 83 a^{2} - 109 a - 102\) , \( -189 a^{5} + 106 a^{4} + 961 a^{3} - 316 a^{2} - 926 a - 97\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{5}-5a^{3}-a^{2}+3a+1\right){x}^{2}+\left(-14a^{5}-14a^{4}+84a^{3}+83a^{2}-109a-102\right){x}-189a^{5}+106a^{4}+961a^{3}-316a^{2}-926a-97$ |
| 31.1-c3 |
31.1-c |
$4$ |
$4$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{4} \) |
$91.58448$ |
$(-a^5+5a^3-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$24.05897029$ |
1.00006 |
\( \frac{148599407106618710023544430465}{923521} a^{5} - \frac{51162067164523519616985613951}{923521} a^{4} - \frac{776544246975688503097892288522}{923521} a^{3} + \frac{85213862179278656941786180477}{923521} a^{2} + \frac{25770070044101319817576470702}{29791} a + \frac{226625478544070566211027844328}{923521} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + a - 2\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 8 a^{2} + 4 a - 4\) , \( 0\) , \( 29 a^{5} - 43 a^{4} - 105 a^{3} + 123 a^{2} + 61 a - 61\) , \( 78 a^{5} - 175 a^{4} - 139 a^{3} + 291 a^{2} + 77 a - 115\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+a-2\right){x}{y}={x}^{3}+\left(2a^{5}-2a^{4}-9a^{3}+8a^{2}+4a-4\right){x}^{2}+\left(29a^{5}-43a^{4}-105a^{3}+123a^{2}+61a-61\right){x}+78a^{5}-175a^{4}-139a^{3}+291a^{2}+77a-115$ |
| 31.1-c4 |
31.1-c |
$4$ |
$4$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$91.58448$ |
$(-a^5+5a^3-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$192.4717623$ |
1.00006 |
\( \frac{959737921004117219213596641}{31} a^{5} + \frac{1004563318667521336749896161}{31} a^{4} - \frac{2742643960681810144259812298}{31} a^{3} - \frac{1774433818463953428848303523}{31} a^{2} + 37643402810618935845636590 a + \frac{468918340227326770581313560}{31} \) |
\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 6 a - 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a\) , \( a^{4} - 4 a^{2} + a + 2\) , \( -74 a^{5} + 74 a^{4} + 339 a^{3} - 244 a^{2} - 243 a - 44\) , \( -500 a^{5} + 472 a^{4} + 2228 a^{3} - 1549 a^{2} - 1348 a - 204\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-9a^{3}+4a^{2}+6a-3\right){x}{y}+\left(a^{4}-4a^{2}+a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a\right){x}^{2}+\left(-74a^{5}+74a^{4}+339a^{3}-244a^{2}-243a-44\right){x}-500a^{5}+472a^{4}+2228a^{3}-1549a^{2}-1348a-204$ |
| 31.2-a1 |
31.2-a |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$91.58448$ |
$(a^4-a^3-5a^2+3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.003877036$ |
$18734.43254$ |
2.26437 |
\( -\frac{5372728560}{923521} a^{5} + \frac{1546070652}{923521} a^{4} + \frac{28593400492}{923521} a^{3} - \frac{1553896830}{923521} a^{2} - \frac{30454940445}{923521} a - \frac{9195678142}{923521} \) |
\( \bigl[a^{4} - 3 a^{2} + a - 1\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 4 a - 5\) , \( a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( a^{3} + 2 a^{2} - 6 a + 2\) , \( 4 a^{5} - 5 a^{4} - 12 a^{3} + 15 a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a-1\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){y}={x}^{3}+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+4a-5\right){x}^{2}+\left(a^{3}+2a^{2}-6a+2\right){x}+4a^{5}-5a^{4}-12a^{3}+15a^{2}+3a-5$ |
| 47.1-a1 |
47.1-a |
$4$ |
$4$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( 47^{4} \) |
$94.81635$ |
$(a^5-a^4-4a^3+4a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$32.65567636$ |
1.35739 |
\( -\frac{239523065600391312345982}{4879681} a^{5} - \frac{92745950730456822976455}{4879681} a^{4} + \frac{1069070700534264670095929}{4879681} a^{3} + \frac{524880302626165548039899}{4879681} a^{2} - \frac{469955941031294527229375}{4879681} a - \frac{172733643671563536452835}{4879681} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + a - 2\) , \( -a^{4} + 5 a^{2} - 3\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 6 a - 2\) , \( -60 a^{5} + 84 a^{4} + 210 a^{3} - 318 a^{2} + 13 a + 37\) , \( -358 a^{5} + 547 a^{4} + 1214 a^{3} - 2098 a^{2} + 208 a + 319\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+a-2\right){x}{y}+\left(2a^{5}-a^{4}-9a^{3}+4a^{2}+6a-2\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-3\right){x}^{2}+\left(-60a^{5}+84a^{4}+210a^{3}-318a^{2}+13a+37\right){x}-358a^{5}+547a^{4}+1214a^{3}-2098a^{2}+208a+319$ |
| 47.1-a2 |
47.1-a |
$4$ |
$4$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( -47 \) |
$94.81635$ |
$(a^5-a^4-4a^3+4a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$16719.70629$ |
1.35739 |
\( -\frac{314882}{47} a^{5} + \frac{291991}{47} a^{4} + \frac{850795}{47} a^{3} - \frac{149973}{47} a^{2} - \frac{258541}{47} a + \frac{48201}{47} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( -a^{4} + 5 a^{2} - 4\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 8 a^{2} + 5 a - 3\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 4\) , \( 16 a^{5} + 17 a^{4} - 47 a^{3} - 31 a^{2} + 23 a + 6\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-2\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+8a^{2}+5a-3\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-4\right){x}^{2}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+5a-4\right){x}+16a^{5}+17a^{4}-47a^{3}-31a^{2}+23a+6$ |
| 47.1-a3 |
47.1-a |
$4$ |
$4$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$94.81635$ |
$(a^5-a^4-4a^3+4a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$2089.963287$ |
1.35739 |
\( -\frac{800826235730}{2209} a^{5} + \frac{1672321121383}{2209} a^{4} + \frac{574341648699}{2209} a^{3} - \frac{1394105750193}{2209} a^{2} + \frac{76684984327}{2209} a + \frac{175128065644}{2209} \) |
\( \bigl[a^{2} - 2\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 9 a^{2} - 4 a + 4\) , \( a^{5} - 4 a^{3} + a^{2} + a - 3\) , \( -640 a^{5} + 216 a^{4} + 3345 a^{3} - 347 a^{2} - 3444 a - 992\) , \( 4631 a^{5} - 1611 a^{4} - 24188 a^{3} + 2739 a^{2} + 24854 a + 6981\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+a-3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-9a^{2}-4a+4\right){x}^{2}+\left(-640a^{5}+216a^{4}+3345a^{3}-347a^{2}-3444a-992\right){x}+4631a^{5}-1611a^{4}-24188a^{3}+2739a^{2}+24854a+6981$ |
| 47.1-a4 |
47.1-a |
$4$ |
$4$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( -47 \) |
$94.81635$ |
$(a^5-a^4-4a^3+4a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$261.2454109$ |
1.35739 |
\( -\frac{189659136243447821918}{47} a^{5} + \frac{549799724355498772041}{47} a^{4} - \frac{95709927534834499511}{47} a^{3} - \frac{576894450215570965493}{47} a^{2} + \frac{147159572937485065425}{47} a + \frac{99879321213836341917}{47} \) |
\( \bigl[a + 1\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 11 a^{2} - 6 a + 3\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a - 1\) , \( 21 a^{5} - 24 a^{4} - 64 a^{3} + 75 a^{2} - 9 a - 80\) , \( 258 a^{5} - 185 a^{4} - 1121 a^{3} + 481 a^{2} + 835 a - 133\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a-1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+9a^{3}-11a^{2}-6a+3\right){x}^{2}+\left(21a^{5}-24a^{4}-64a^{3}+75a^{2}-9a-80\right){x}+258a^{5}-185a^{4}-1121a^{3}+481a^{2}+835a-133$ |
| 47.1-b1 |
47.1-b |
$4$ |
$6$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{2} \) |
$94.81635$ |
$(a^5-a^4-4a^3+4a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \) |
$2.559920007$ |
$2.891446987$ |
2.33639 |
\( \frac{3376891207325650952823350395}{2209} a^{5} - \frac{6289491628967718798899573900}{2209} a^{4} - \frac{11459710362054993341405221259}{2209} a^{3} + \frac{23391672780432152222602974500}{2209} a^{2} - \frac{3291081705128924712103742354}{2209} a - \frac{3915193495592384699887630865}{2209} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 2\) , \( 767 a^{5} - 1165 a^{4} - 3414 a^{3} + 4728 a^{2} + 2262 a - 2760\) , \( 16792 a^{5} - 23007 a^{4} - 75423 a^{3} + 94591 a^{2} + 51674 a - 53458\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+2a-2\right){y}={x}^{3}+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}^{2}+\left(767a^{5}-1165a^{4}-3414a^{3}+4728a^{2}+2262a-2760\right){x}+16792a^{5}-23007a^{4}-75423a^{3}+94591a^{2}+51674a-53458$ |
| 47.1-b2 |
47.1-b |
$4$ |
$6$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{3} \) |
$94.81635$ |
$(a^5-a^4-4a^3+4a^2-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.426653334$ |
$8431.459415$ |
2.33639 |
\( -\frac{3507812068}{103823} a^{5} - \frac{315715167}{103823} a^{4} + \frac{8826891877}{103823} a^{3} + \frac{822025516}{103823} a^{2} - \frac{2961081785}{103823} a - \frac{406299355}{103823} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + a - 3\) , \( a^{5} - 4 a^{3} + 2 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 2\) , \( 6 a^{5} - 3 a^{4} - 26 a^{3} + 16 a^{2} + 21 a - 9\) , \( -a^{5} + 4 a^{4} + 8 a^{3} - 11 a^{2} - 8 a + 2\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+a-3\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a-2\right){y}={x}^{3}+\left(a^{5}-4a^{3}+2a-1\right){x}^{2}+\left(6a^{5}-3a^{4}-26a^{3}+16a^{2}+21a-9\right){x}-a^{5}+4a^{4}+8a^{3}-11a^{2}-8a+2$ |
| 47.1-b3 |
47.1-b |
$4$ |
$6$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{6} \) |
$94.81635$ |
$(a^5-a^4-4a^3+4a^2-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.853306669$ |
$2107.864853$ |
2.33639 |
\( \frac{139303762000028106410}{10779215329} a^{5} + \frac{144651335296590529675}{10779215329} a^{4} - \frac{398301886856690377987}{10779215329} a^{3} - \frac{254059666624465013527}{10779215329} a^{2} + \frac{168506876713509452114}{10779215329} a + \frac{67406258267820761856}{10779215329} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + a - 3\) , \( a^{5} - 4 a^{3} + 2 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 2\) , \( a^{5} - 3 a^{4} - 6 a^{3} + 31 a^{2} + 16 a - 59\) , \( 4 a^{5} - 18 a^{4} - 24 a^{3} + 118 a^{2} + 43 a - 176\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+a-3\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a-2\right){y}={x}^{3}+\left(a^{5}-4a^{3}+2a-1\right){x}^{2}+\left(a^{5}-3a^{4}-6a^{3}+31a^{2}+16a-59\right){x}+4a^{5}-18a^{4}-24a^{3}+118a^{2}+43a-176$ |
| 47.1-b4 |
47.1-b |
$4$ |
$6$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( -47 \) |
$94.81635$ |
$(a^5-a^4-4a^3+4a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1.279960003$ |
$11.56578794$ |
2.33639 |
\( -\frac{21417905398977605}{47} a^{5} + \frac{62004666093510408}{47} a^{4} - \frac{10624618770251898}{47} a^{3} - \frac{65152171397191321}{47} a^{2} + \frac{16575370430512357}{47} a + \frac{11272985421638474}{47} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} - 4\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( -19 a^{5} + 38 a^{4} + 85 a^{3} - 167 a^{2} - 8 a + 12\) , \( -105 a^{5} + 197 a^{4} + 473 a^{3} - 942 a^{2} + 53 a + 129\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+9a^{2}-4\right){x}^{2}+\left(-19a^{5}+38a^{4}+85a^{3}-167a^{2}-8a+12\right){x}-105a^{5}+197a^{4}+473a^{3}-942a^{2}+53a+129$ |
| 49.1-a1 |
49.1-a |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{14} \) |
$95.14619$ |
$(a^5-2a^4-5a^3+7a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1384.148073$ |
1.79796 |
\( \frac{7276612344201570}{823543} a^{5} + \frac{2816047654779374}{823543} a^{4} - \frac{32477199071902533}{823543} a^{3} - \frac{15939419409793606}{823543} a^{2} + \frac{14275065920439475}{823543} a + \frac{5246284168272092}{823543} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 1\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 6 a - 7\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a - 1\) , \( -88 a^{5} + 34 a^{4} + 458 a^{3} - 68 a^{2} - 465 a - 120\) , \( 658 a^{5} - 224 a^{4} - 3439 a^{3} + 364 a^{2} + 3542 a + 1014\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+2a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a-1\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+6a-7\right){x}^{2}+\left(-88a^{5}+34a^{4}+458a^{3}-68a^{2}-465a-120\right){x}+658a^{5}-224a^{4}-3439a^{3}+364a^{2}+3542a+1014$ |
| 49.2-a1 |
49.2-a |
$2$ |
$3$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$95.14619$ |
$(a^4-4a^2+a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.013940662$ |
$12990.64016$ |
2.82288 |
\( 24164258357939329603 a^{5} - 32090567672134595043 a^{4} - 110295011211469229354 a^{3} + 132835771594028505313 a^{2} + 77248781181165510499 a - 73667499983669418847 \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 2\) , \( a\) , \( 9 a^{5} + 10 a^{4} - 36 a^{3} - 43 a^{2} + 3 a - 6\) , \( -49 a^{5} - 33 a^{4} + 208 a^{3} + 164 a^{2} - 53 a - 19\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+2a-2\right){x}^{2}+\left(9a^{5}+10a^{4}-36a^{3}-43a^{2}+3a-6\right){x}-49a^{5}-33a^{4}+208a^{3}+164a^{2}-53a-19$ |
| 49.2-a2 |
49.2-a |
$2$ |
$3$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$95.14619$ |
$(a^4-4a^2+a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.004646887$ |
$38971.92049$ |
2.82288 |
\( 1285592 a^{5} - 1709472 a^{4} - 5867135 a^{3} + 7077626 a^{2} + 4106851 a - 3927865 \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 2\) , \( a\) , \( -a^{5} + 4 a^{3} + 2 a^{2} - 2 a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+2a-2\right){x}^{2}+\left(-a^{5}+4a^{3}+2a^{2}-2a-1\right){x}$ |
| 49.2-b1 |
49.2-b |
$2$ |
$7$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{8} \) |
$95.14619$ |
$(a^4-4a^2+a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$7$ |
7B.6.3 |
$1$ |
\( 1 \) |
$1$ |
$1081.567760$ |
1.40492 |
\( -21437955273398086628814342060 a^{5} - 8296492504833651562385453152 a^{4} + 95682539786756414754531486072 a^{3} + 46959878613528243860092427239 a^{2} - 42056416375390440919728940937 a - 15456346448131269056429661858 \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 11 a^{2} + 5 a - 3\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 5 a - 6\) , \( -150 a^{5} + 288 a^{4} + 503 a^{3} - 1083 a^{2} + 192 a + 167\) , \( 1413 a^{5} - 2764 a^{4} - 4519 a^{3} + 10175 a^{2} - 2425 a - 1163\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-3\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+5a-6\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-9a^{3}+11a^{2}+5a-3\right){x}^{2}+\left(-150a^{5}+288a^{4}+503a^{3}-1083a^{2}+192a+167\right){x}+1413a^{5}-2764a^{4}-4519a^{3}+10175a^{2}-2425a-1163$ |
| 49.2-b2 |
49.2-b |
$2$ |
$7$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{8} \) |
$95.14619$ |
$(a^4-4a^2+a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$1081.567760$ |
1.40492 |
\( -466893 a^{5} + 96319 a^{4} + 2480115 a^{3} + 52414 a^{2} - 2640289 a - 1001005 \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 3\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( 6 a^{5} - 6 a^{4} - 24 a^{3} + 27 a^{2} + 16 a - 15\) , \( 6 a^{5} - 5 a^{4} - 22 a^{3} + 21 a^{2} + 14 a - 13\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+a-2\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+2a-3\right){x}^{2}+\left(6a^{5}-6a^{4}-24a^{3}+27a^{2}+16a-15\right){x}+6a^{5}-5a^{4}-22a^{3}+21a^{2}+14a-13$ |
| 49.2-c1 |
49.2-c |
$2$ |
$7$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{2} \) |
$95.14619$ |
$(a^4-4a^2+a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$7$ |
7B.1.3 |
$49$ |
\( 1 \) |
$1.100846541$ |
$6.680361328$ |
2.80848 |
\( -21437955273398086628814342060 a^{5} - 8296492504833651562385453152 a^{4} + 95682539786756414754531486072 a^{3} + 46959878613528243860092427239 a^{2} - 42056416375390440919728940937 a - 15456346448131269056429661858 \) |
\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 6 a - 4\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( 23 a^{5} + 6 a^{4} - 108 a^{3} - 42 a^{2} + 62 a + 17\) , \( 85 a^{5} + 42 a^{4} - 373 a^{3} - 245 a^{2} + 97 a + 41\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-9a^{3}+5a^{2}+6a-4\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(23a^{5}+6a^{4}-108a^{3}-42a^{2}+62a+17\right){x}+85a^{5}+42a^{4}-373a^{3}-245a^{2}+97a+41$ |
| 49.2-c2 |
49.2-c |
$2$ |
$7$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{2} \) |
$95.14619$ |
$(a^4-4a^2+a+2)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$0.157263791$ |
$112276.8328$ |
2.80848 |
\( -466893 a^{5} + 96319 a^{4} + 2480115 a^{3} + 52414 a^{2} - 2640289 a - 1001005 \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 5 a^{2} + 2 a - 4\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 5 a - 5\) , \( 2 a^{5} - 2 a^{4} - 7 a^{3} + 11 a^{2} + 3 a - 6\) , \( 5 a^{5} - a^{4} - 20 a^{3} + 6 a^{2} + 10 a - 5\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+5a^{2}+2a-4\right){x}{y}+\left(2a^{5}-a^{4}-9a^{3}+5a^{2}+5a-5\right){y}={x}^{3}+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){x}^{2}+\left(2a^{5}-2a^{4}-7a^{3}+11a^{2}+3a-6\right){x}+5a^{5}-a^{4}-20a^{3}+6a^{2}+10a-5$ |
| 49.2-d1 |
49.2-d |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{16} \) |
$95.14619$ |
$(a^4-4a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.140992452$ |
$2368.483818$ |
2.60264 |
\( -\frac{6378555847697446312}{282475249} a^{5} - \frac{2474411833285999287}{282475249} a^{4} + \frac{28471855515534194816}{282475249} a^{3} + \frac{13996124332632398039}{282475249} a^{2} - \frac{12521297730192365783}{282475249} a - \frac{4603543349670581566}{282475249} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 3 a - 2\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 5 a - 5\) , \( 27 a^{5} - 81 a^{4} - 85 a^{3} + 376 a^{2} - 22 a - 297\) , \( 242 a^{5} - 536 a^{4} - 965 a^{3} + 2432 a^{2} + 294 a - 1763\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+2a-3\right){x}{y}+\left(2a^{5}-a^{4}-9a^{3}+5a^{2}+5a-5\right){y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-3a-2\right){x}^{2}+\left(27a^{5}-81a^{4}-85a^{3}+376a^{2}-22a-297\right){x}+242a^{5}-536a^{4}-965a^{3}+2432a^{2}+294a-1763$ |
| 49.2-d2 |
49.2-d |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{11} \) |
$95.14619$ |
$(a^4-4a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.070496226$ |
$4736.967637$ |
2.60264 |
\( \frac{1519176145}{16807} a^{5} + \frac{970371936}{16807} a^{4} - \frac{5971587107}{16807} a^{3} - \frac{3315408956}{16807} a^{2} + \frac{2656017515}{16807} a + \frac{1004044424}{16807} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 3 a - 4\) , \( a^{5} - a^{4} - 4 a^{3} + 5 a^{2} + a - 4\) , \( -a^{5} + 2 a^{4} - 8 a^{2} + 5 a + 1\) , \( -4 a^{4} - a^{3} + 15 a^{2} - 4 a - 7\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+5a^{2}+a-4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+9a^{2}+3a-4\right){x}^{2}+\left(-a^{5}+2a^{4}-8a^{2}+5a+1\right){x}-4a^{4}-a^{3}+15a^{2}-4a-7$ |
| 59.1-a1 |
59.1-a |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
59.1 |
\( 59 \) |
\( -59 \) |
$96.63017$ |
$(a^5-5a^3-a^2+5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.001387074$ |
$243270.9793$ |
2.62989 |
\( -\frac{2155963}{59} a^{5} + \frac{2798408}{59} a^{4} + \frac{8836800}{59} a^{3} - \frac{11572938}{59} a^{2} - \frac{4048399}{59} a + \frac{4872625}{59} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 6 a - 5\) , \( -a^{2} + 3\) , \( a^{5} - 5 a^{3} + 4 a\) , \( -10 a^{5} + 14 a^{4} + 46 a^{3} - 59 a^{2} - 33 a + 34\) , \( -14 a^{5} + 19 a^{4} + 64 a^{3} - 79 a^{2} - 45 a + 44\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+6a-5\right){x}{y}+\left(a^{5}-5a^{3}+4a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-10a^{5}+14a^{4}+46a^{3}-59a^{2}-33a+34\right){x}-14a^{5}+19a^{4}+64a^{3}-79a^{2}-45a+44$ |
| 67.1-a1 |
67.1-a |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
67.1 |
\( 67 \) |
\( -67 \) |
$97.65953$ |
$(a^5-a^4-5a^3+5a^2+5a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.008824863$ |
$38394.88244$ |
2.64076 |
\( -\frac{293657}{67} a^{5} + \frac{844369}{67} a^{4} - \frac{137481}{67} a^{3} - \frac{966413}{67} a^{2} + \frac{347718}{67} a + \frac{215682}{67} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 5 a^{2} + 2 a - 3\) , \( -a^{3} + 2 a\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 1\) , \( -a^{3} + 2 a\) , \( 0\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+5a^{2}+2a-3\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+2a-1\right){y}={x}^{3}+\left(-a^{3}+2a\right){x}^{2}+\left(-a^{3}+2a\right){x}$ |
| 67.2-a1 |
67.2-a |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
67.2 |
\( 67 \) |
\( 67^{5} \) |
$97.65953$ |
$(-a^4+a^3+5a^2-2a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.020626064$ |
$3516.974403$ |
2.82685 |
\( -\frac{184392193330736}{1350125107} a^{5} + \frac{272761023393987}{1350125107} a^{4} + \frac{846288828316947}{1350125107} a^{3} - \frac{1135825837953888}{1350125107} a^{2} - \frac{622639562545579}{1350125107} a + \frac{611921133846794}{1350125107} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 5 a^{2} + 2 a - 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 5 a - 3\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 6 a - 3\) , \( 4 a^{5} - 3 a^{4} - 19 a^{3} + 11 a^{2} + 14 a - 6\) , \( a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 6 a - 3\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+5a^{2}+2a-4\right){x}{y}+\left(2a^{5}-a^{4}-9a^{3}+4a^{2}+6a-3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+5a-3\right){x}^{2}+\left(4a^{5}-3a^{4}-19a^{3}+11a^{2}+14a-6\right){x}+a^{5}-a^{4}-6a^{3}+3a^{2}+6a-3$ |
| 67.2-b1 |
67.2-b |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
67.2 |
\( 67 \) |
\( 67 \) |
$97.65953$ |
$(-a^4+a^3+5a^2-2a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.002280473$ |
$122461.4129$ |
2.17657 |
\( -\frac{75626}{67} a^{5} + \frac{180467}{67} a^{4} + \frac{112536}{67} a^{3} - \frac{337206}{67} a^{2} - \frac{114765}{67} a + \frac{164450}{67} \) |
\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 5 a - 5\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 6 a - 2\) , \( a^{2} - 1\) , \( -4 a^{5} + 17 a^{3} - a^{2} - 6 a + 6\) , \( 11 a^{5} - 4 a^{4} - 60 a^{3} + 5 a^{2} + 70 a + 26\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-9a^{3}+5a^{2}+5a-5\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+6a-2\right){x}^{2}+\left(-4a^{5}+17a^{3}-a^{2}-6a+6\right){x}+11a^{5}-4a^{4}-60a^{3}+5a^{2}+70a+26$ |
| 73.2-a1 |
73.2-a |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( - 73^{2} \) |
$98.36003$ |
$(-a^5+2a^4+5a^3-8a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.407837542$ |
$1954.318194$ |
3.10599 |
\( \frac{27717869787519429954038}{5329} a^{5} - \frac{51624793130186400377021}{5329} a^{4} - \frac{94062479398000747462595}{5329} a^{3} + \frac{192001252167547026433718}{5329} a^{2} - \frac{27013536581854090760860}{5329} a - \frac{32136310245606568782898}{5329} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 3\) , \( -a^{5} + 4 a^{3} - a^{2} - 2 a + 4\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 3\) , \( -50 a^{5} + 16 a^{4} + 254 a^{3} - 32 a^{2} - 245 a - 54\) , \( 20 a^{5} - 2 a^{4} - 112 a^{3} - 18 a^{2} + 134 a + 69\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+2a-3\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+5a-3\right){y}={x}^{3}+\left(-a^{5}+4a^{3}-a^{2}-2a+4\right){x}^{2}+\left(-50a^{5}+16a^{4}+254a^{3}-32a^{2}-245a-54\right){x}+20a^{5}-2a^{4}-112a^{3}-18a^{2}+134a+69$ |
| 73.2-a2 |
73.2-a |
$2$ |
$2$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( 73 \) |
$98.36003$ |
$(-a^5+2a^4+5a^3-8a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.203918771$ |
$7817.272777$ |
3.10599 |
\( \frac{70966195776}{73} a^{5} - \frac{132175265612}{73} a^{4} - \frac{240828273073}{73} a^{3} + \frac{491581931638}{73} a^{2} - \frac{69163837407}{73} a - \frac{82278199639}{73} \) |
\( \bigl[a^{2} + a - 1\) , \( -2 a^{5} + 2 a^{4} + 9 a^{3} - 7 a^{2} - 5 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 4\) , \( -23 a^{5} + 45 a^{4} + 78 a^{3} - 165 a^{2} + 27 a + 27\) , \( -87 a^{5} + 166 a^{4} + 294 a^{3} - 614 a^{2} + 94 a + 99\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+5a-4\right){y}={x}^{3}+\left(-2a^{5}+2a^{4}+9a^{3}-7a^{2}-5a+2\right){x}^{2}+\left(-23a^{5}+45a^{4}+78a^{3}-165a^{2}+27a+27\right){x}-87a^{5}+166a^{4}+294a^{3}-614a^{2}+94a+99$ |
| 73.2-b1 |
73.2-b |
$4$ |
$6$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( 73^{9} \) |
$98.36003$ |
$(-a^5+2a^4+5a^3-8a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3^{2} \) |
$0.136290711$ |
$122.2172354$ |
2.62889 |
\( -\frac{819409026299375534395416}{58871586708267913} a^{5} - \frac{170251602571138272825926}{58871586708267913} a^{4} + \frac{3968508698135623357582134}{58871586708267913} a^{3} + \frac{1769334738717973761105523}{58871586708267913} a^{2} - \frac{1771210861015578326012193}{58871586708267913} a - \frac{587323218030274014006283}{58871586708267913} \) |
\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 5 a - 3\) , \( -a^{2} + 3\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 5 a - 4\) , \( -15 a^{5} + 33 a^{4} + 46 a^{3} - 126 a^{2} + 28 a + 25\) , \( -62 a^{5} + 155 a^{4} + 190 a^{3} - 590 a^{2} + 117 a + 98\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-9a^{3}+4a^{2}+5a-3\right){x}{y}+\left(2a^{5}-a^{4}-9a^{3}+5a^{2}+5a-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-15a^{5}+33a^{4}+46a^{3}-126a^{2}+28a+25\right){x}-62a^{5}+155a^{4}+190a^{3}-590a^{2}+117a+98$ |
| 73.2-b2 |
73.2-b |
$4$ |
$6$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( 73^{3} \) |
$98.36003$ |
$(-a^5+2a^4+5a^3-8a^2-4a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.045430237$ |
$89096.36466$ |
2.62889 |
\( \frac{896212872}{389017} a^{5} - \frac{2330492990}{389017} a^{4} - \frac{1852149899}{389017} a^{3} + \frac{8270889498}{389017} a^{2} - \frac{4711142963}{389017} a + \frac{266102902}{389017} \) |
\( \bigl[1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{5} - 4 a^{3} + 2 a\) , \( 3 a^{5} - 6 a^{4} - 13 a^{3} + 25 a^{2} + 8 a - 12\) , \( -5 a^{5} + 7 a^{4} + 22 a^{3} - 30 a^{2} - 15 a + 16\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}-4a^{3}+2a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}^{2}+\left(3a^{5}-6a^{4}-13a^{3}+25a^{2}+8a-12\right){x}-5a^{5}+7a^{4}+22a^{3}-30a^{2}-15a+16$ |
| 73.2-b3 |
73.2-b |
$4$ |
$6$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( 73^{18} \) |
$98.36003$ |
$(-a^5+2a^4+5a^3-8a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$0.272581422$ |
$30.55430887$ |
2.62889 |
\( \frac{11372231335975499487548409217734686005}{3465863721549107204083472585375569} a^{5} + \frac{4264801553412190253107013260252317742}{3465863721549107204083472585375569} a^{4} - \frac{54440949571368897149149981857454108168}{3465863721549107204083472585375569} a^{3} - \frac{21586698376877736997265390233169345179}{3465863721549107204083472585375569} a^{2} + \frac{42530472932329554348989398674037044375}{3465863721549107204083472585375569} a + \frac{20838781984133769652556699379271747799}{3465863721549107204083472585375569} \) |
\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 5 a - 3\) , \( -a^{2} + 3\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 5 a - 4\) , \( -15 a^{5} + 13 a^{4} + 71 a^{3} - 46 a^{2} - 52 a - 10\) , \( -178 a^{5} + 317 a^{4} + 650 a^{3} - 1170 a^{2} + 5 a + 137\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-9a^{3}+4a^{2}+5a-3\right){x}{y}+\left(2a^{5}-a^{4}-9a^{3}+5a^{2}+5a-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-15a^{5}+13a^{4}+71a^{3}-46a^{2}-52a-10\right){x}-178a^{5}+317a^{4}+650a^{3}-1170a^{2}+5a+137$ |
| 73.2-b4 |
73.2-b |
$4$ |
$6$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( 73^{6} \) |
$98.36003$ |
$(-a^5+2a^4+5a^3-8a^2-4a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.090860474$ |
$22274.09116$ |
2.62889 |
\( -\frac{1750397764286997144}{151334226289} a^{5} + \frac{2384110649186678931}{151334226289} a^{4} + \frac{7888305624092684601}{151334226289} a^{3} - \frac{9728289241621098752}{151334226289} a^{2} - \frac{5474432982410677682}{151334226289} a + \frac{5421863886826175453}{151334226289} \) |
\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 5 a - 3\) , \( -a^{2} + 3\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 5 a - 4\) , \( -5 a^{5} - 2 a^{4} + 26 a^{3} + 9 a^{2} - 22 a - 5\) , \( 2 a^{5} - 14 a^{4} - 4 a^{3} + 56 a^{2} - 10 a - 9\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-9a^{3}+4a^{2}+5a-3\right){x}{y}+\left(2a^{5}-a^{4}-9a^{3}+5a^{2}+5a-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-5a^{5}-2a^{4}+26a^{3}+9a^{2}-22a-5\right){x}+2a^{5}-14a^{4}-4a^{3}+56a^{2}-10a-9$ |
| 83.1-a1 |
83.1-a |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
83.1 |
\( 83 \) |
\( -83 \) |
$99.41797$ |
$(-2a^5+a^4+9a^3-4a^2-6a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.005387149$ |
$80327.79265$ |
3.37267 |
\( \frac{2284010860}{83} a^{5} + \frac{884600390}{83} a^{4} - \frac{10195196217}{83} a^{3} - \frac{5005268270}{83} a^{2} + \frac{4484649386}{83} a + \frac{1645381845}{83} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 3 a - 2\) , \( a^{2} - 2\) , \( -a^{5} + 2 a^{4} + 6 a^{3} + a - 2\) , \( a^{5} + 7 a^{2} - 2 a - 2\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+3a-2\right){x}^{2}+\left(-a^{5}+2a^{4}+6a^{3}+a-2\right){x}+a^{5}+7a^{2}-2a-2$ |
| 83.1-b1 |
83.1-b |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
83.1 |
\( 83 \) |
\( -83 \) |
$99.41797$ |
$(-2a^5+a^4+9a^3-4a^2-6a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.026258286$ |
$14031.16581$ |
2.87149 |
\( -\frac{166519119719}{83} a^{5} + \frac{57331816854}{83} a^{4} + \frac{870188329038}{83} a^{3} - \frac{95490374048}{83} a^{2} - \frac{895208628138}{83} a - \frac{253954106815}{83} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 4\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 5 a - 2\) , \( 3 a^{5} - 14 a^{3} - a^{2} + 10 a + 1\) , \( -3 a^{5} - a^{4} + 13 a^{3} + 6 a^{2} - 5 a - 4\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a-1\right){x}{y}+\left(2a^{5}-a^{4}-9a^{3}+4a^{2}+5a-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-4\right){x}^{2}+\left(3a^{5}-14a^{3}-a^{2}+10a+1\right){x}-3a^{5}-a^{4}+13a^{3}+6a^{2}-5a-4$ |
| 83.1-c1 |
83.1-c |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
83.1 |
\( 83 \) |
\( 83^{4} \) |
$99.41797$ |
$(-2a^5+a^4+9a^3-4a^2-6a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.007707327$ |
$12401.08843$ |
2.97969 |
\( \frac{15736963093640}{47458321} a^{5} - \frac{44917566551496}{47458321} a^{4} + \frac{6514884455608}{47458321} a^{3} + \frac{47332089860599}{47458321} a^{2} - \frac{11320884612420}{47458321} a - \frac{8429605989992}{47458321} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 4\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 8 a^{2} - a + 2\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 6 a - 4\) , \( 2 a^{5} + 5 a^{4} - 10 a^{3} - 23 a^{2} + 6 a + 7\) , \( -21 a^{5} + 13 a^{4} + 84 a^{3} - 42 a^{2} - 17 a + 6\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-4\right){x}{y}+\left(2a^{5}-a^{4}-9a^{3}+5a^{2}+6a-4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-8a^{2}-a+2\right){x}^{2}+\left(2a^{5}+5a^{4}-10a^{3}-23a^{2}+6a+7\right){x}-21a^{5}+13a^{4}+84a^{3}-42a^{2}-17a+6$ |
| 83.1-d1 |
83.1-d |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
83.1 |
\( 83 \) |
\( -83 \) |
$99.41797$ |
$(-2a^5+a^4+9a^3-4a^2-6a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.005613072$ |
$70481.43116$ |
3.08335 |
\( \frac{46638196}{83} a^{5} + \frac{119264171}{83} a^{4} - \frac{90683712}{83} a^{3} - \frac{273899140}{83} a^{2} + \frac{36697985}{83} a + \frac{37204710}{83} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 5 a - 6\) , \( a^{5} - 5 a^{3} + a^{2} + 3 a - 4\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -11 a^{5} + 14 a^{4} + 48 a^{3} - 56 a^{2} - 32 a + 32\) , \( -23 a^{5} + 31 a^{4} + 105 a^{3} - 128 a^{2} - 76 a + 72\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+5a-6\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(a^{5}-5a^{3}+a^{2}+3a-4\right){x}^{2}+\left(-11a^{5}+14a^{4}+48a^{3}-56a^{2}-32a+32\right){x}-23a^{5}+31a^{4}+105a^{3}-128a^{2}-76a+72$ |
| 91.1-a1 |
91.1-a |
$1$ |
$1$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 7^{2} \cdot 13 \) |
$100.18326$ |
$(a^4-4a^2+a+2), (-a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$554.0386088$ |
1.43935 |
\( -\frac{3112787549}{637} a^{5} + \frac{5234540113}{637} a^{4} + \frac{12681840034}{637} a^{3} - \frac{23676316917}{637} a^{2} + \frac{3147513197}{637} a + \frac{3950621782}{637} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 8 a^{2} + 5 a - 4\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( a^{4} - 4 a^{2} + 2\) , \( 3 a^{5} - 16 a^{3} - 3 a^{2} + 18 a + 9\) , \( 9 a^{5} - 4 a^{4} - 47 a^{3} + 9 a^{2} + 48 a + 11\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+8a^{2}+5a-4\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-2\right){x}^{2}+\left(3a^{5}-16a^{3}-3a^{2}+18a+9\right){x}+9a^{5}-4a^{4}-47a^{3}+9a^{2}+48a+11$ |
| 91.1-b1 |
91.1-b |
$4$ |
$14$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
91.1 |
\( 7 \cdot 13 \) |
\( - 7^{7} \cdot 13^{2} \) |
$100.18326$ |
$(a^4-4a^2+a+2), (-a^3+3a)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.393687975$ |
$15349.55474$ |
3.36409 |
\( -\frac{75920719558025}{139178767} a^{5} + \frac{26110568103036}{139178767} a^{4} + \frac{396790644808426}{139178767} a^{3} - \frac{43416547811453}{139178767} a^{2} - \frac{408239914338619}{139178767} a - \frac{115757315220418}{139178767} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( -a^{5} + 4 a^{3} + a^{2}\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a - 2\) , \( 2 a^{4} + 7 a^{3} + 4 a^{2} - 4 a - 1\) , \( 3 a^{5} + 6 a^{4} - a^{3} - 2 a^{2} + a - 1\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a-2\right){y}={x}^{3}+\left(-a^{5}+4a^{3}+a^{2}\right){x}^{2}+\left(2a^{4}+7a^{3}+4a^{2}-4a-1\right){x}+3a^{5}+6a^{4}-a^{3}-2a^{2}+a-1$ |
| 91.1-b2 |
91.1-b |
$4$ |
$14$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
91.1 |
\( 7 \cdot 13 \) |
\( - 7^{14} \cdot 13 \) |
$100.18326$ |
$(a^4-4a^2+a+2), (-a^3+3a)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.787375951$ |
$7674.777372$ |
3.36409 |
\( \frac{10187271959655082587569549}{8816899947037} a^{5} - \frac{3507428677668001732667496}{8816899947037} a^{4} - \frac{53236198872825797367425899}{8816899947037} a^{3} + \frac{5841858552819251017747808}{8816899947037} a^{2} + \frac{54766895766825615926943448}{8816899947037} a + \frac{15536370509879099207711495}{8816899947037} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( -a^{5} + 4 a^{3} + a^{2}\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a - 2\) , \( 5 a^{5} - 3 a^{4} - 13 a^{3} + 24 a^{2} + 11 a - 16\) , \( 16 a^{5} + 2 a^{4} - 55 a^{3} + 31 a^{2} + 32 a - 21\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a-2\right){y}={x}^{3}+\left(-a^{5}+4a^{3}+a^{2}\right){x}^{2}+\left(5a^{5}-3a^{4}-13a^{3}+24a^{2}+11a-16\right){x}+16a^{5}+2a^{4}-55a^{3}+31a^{2}+32a-21$ |
| 91.1-b3 |
91.1-b |
$4$ |
$14$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
91.1 |
\( 7 \cdot 13 \) |
\( - 7 \cdot 13^{14} \) |
$100.18326$ |
$(a^4-4a^2+a+2), (-a^3+3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 2 \) |
$2.755815829$ |
$0.130469062$ |
3.36409 |
\( \frac{210494899395329104316882674818601470}{27561634699895023} a^{5} + \frac{220326152901046187397217035121037707}{27561634699895023} a^{4} - \frac{601531540208629141835154188949660818}{27561634699895023} a^{3} - \frac{389178106994375647928627220188772756}{27561634699895023} a^{2} + \frac{255940859747009559786272783613073517}{27561634699895023} a + \frac{102845559693375533397370969339933439}{27561634699895023} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + a - 2\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 4\) , \( a^{2} + a - 2\) , \( 258 a^{5} + 118 a^{4} - 1548 a^{3} - 690 a^{2} + 2039 a + 580\) , \( -20998 a^{5} + 9446 a^{4} + 107566 a^{3} - 21228 a^{2} - 105796 a - 29121\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+5a-4\right){x}^{2}+\left(258a^{5}+118a^{4}-1548a^{3}-690a^{2}+2039a+580\right){x}-20998a^{5}+9446a^{4}+107566a^{3}-21228a^{2}-105796a-29121$ |
| 91.1-b4 |
91.1-b |
$4$ |
$14$ |
6.6.592661.1 |
$6$ |
$[6, 0]$ |
91.1 |
\( 7 \cdot 13 \) |
\( - 7^{2} \cdot 13^{7} \) |
$100.18326$ |
$(a^4-4a^2+a+2), (-a^3+3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 2 \) |
$5.511631659$ |
$0.065234531$ |
3.36409 |
\( -\frac{21597161649790866133606261509753255}{3074677333} a^{5} + \frac{28681417201034137650056150261573678}{3074677333} a^{4} + \frac{98577790071360663809442695639115372}{3074677333} a^{3} - \frac{118723926019387924147249784736135276}{3074677333} a^{2} - \frac{69042235603570084841387147093553420}{3074677333} a + \frac{65841412268351842671192507620649913}{3074677333} \) |
\( \bigl[a^{5} - 4 a^{3} + 2 a - 1\) , \( -a^{5} + a^{4} + 4 a^{3} - 3 a^{2} - 1\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a - 2\) , \( 144 a^{5} - 1196 a^{4} + 370 a^{3} + 1760 a^{2} - 1685 a - 1839\) , \( 2258 a^{5} - 49271 a^{4} + 26550 a^{3} + 54926 a^{2} - 43051 a - 32680\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+2a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-3a^{2}-1\right){x}^{2}+\left(144a^{5}-1196a^{4}+370a^{3}+1760a^{2}-1685a-1839\right){x}+2258a^{5}-49271a^{4}+26550a^{3}+54926a^{2}-43051a-32680$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
