| 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 |
| 3.1-a1 |
3.1-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{6} \) |
$35.23608$ |
$(-a^4+a^3+6a^2+a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$0.023198797$ |
$2657.135355$ |
1.74478643 |
\( \frac{44722187}{729} a^{4} - \frac{58908412}{729} a^{3} - \frac{78297241}{243} a^{2} + \frac{13549633}{243} a + \frac{32710483}{729} \) |
\( \bigl[4 a^{4} - 3 a^{3} - 24 a^{2} - 9 a + 6\) , \( -a^{4} + a^{3} + 5 a^{2} + 3 a - 1\) , \( 4 a^{4} - 3 a^{3} - 24 a^{2} - 9 a + 7\) , \( a^{4} - a^{3} - 6 a^{2} + 2\) , \( 2 a^{4} + a^{3} - 17 a^{2} - 13 a + 8\bigr] \) |
${y}^2+\left(4a^{4}-3a^{3}-24a^{2}-9a+6\right){x}{y}+\left(4a^{4}-3a^{3}-24a^{2}-9a+7\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}+3a-1\right){x}^{2}+\left(a^{4}-a^{3}-6a^{2}+2\right){x}+2a^{4}+a^{3}-17a^{2}-13a+8$ |
| 7.1-a1 |
7.1-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$38.35175$ |
$(-a^4+a^3+6a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.008906923$ |
$8434.695065$ |
2.12647484 |
\( -\frac{176992}{7} a^{4} - \frac{650231}{7} a^{3} - \frac{527910}{7} a^{2} + \frac{177964}{7} a + \frac{100409}{7} \) |
\( \bigl[4 a^{4} - 3 a^{3} - 24 a^{2} - 9 a + 7\) , \( -1\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 2\) , \( 17 a^{4} - 5 a^{3} - 118 a^{2} - 66 a + 53\) , \( 36 a^{4} - 11 a^{3} - 249 a^{2} - 139 a + 115\bigr] \) |
${y}^2+\left(4a^{4}-3a^{3}-24a^{2}-9a+7\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-3a+2\right){y}={x}^{3}-{x}^{2}+\left(17a^{4}-5a^{3}-118a^{2}-66a+53\right){x}+36a^{4}-11a^{3}-249a^{2}-139a+115$ |
| 7.1-b1 |
7.1-b |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$38.35175$ |
$(-a^4+a^3+6a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$262.3685227$ |
1.48526811 |
\( -155833909 a^{4} + \frac{347104006}{7} a^{3} + \frac{7528787059}{7} a^{2} + \frac{4152015626}{7} a - \frac{3529686207}{7} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 2\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 2\) , \( 3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 7\) , \( 7 a^{4} - 2 a^{3} - 39 a^{2} - 43 a - 18\) , \( 12 a^{4} + 4 a^{3} - 76 a^{2} - 108 a - 40\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-11a^{2}-3a+2\right){x}{y}+\left(3a^{4}-2a^{3}-19a^{2}-7a+7\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-11a^{2}-3a+2\right){x}^{2}+\left(7a^{4}-2a^{3}-39a^{2}-43a-18\right){x}+12a^{4}+4a^{3}-76a^{2}-108a-40$ |
| 7.1-c1 |
7.1-c |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$38.35175$ |
$(-a^4+a^3+6a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.017927097$ |
$5745.274813$ |
1.45765224 |
\( \frac{103329}{7} a^{4} - \frac{204989}{7} a^{3} - \frac{474848}{7} a^{2} + 70532 a + \frac{83801}{7} \) |
\( \bigl[4 a^{4} - 3 a^{3} - 24 a^{2} - 9 a + 7\) , \( -a^{2} + 2 a + 1\) , \( 2 a^{4} - 2 a^{3} - 12 a^{2} - a + 4\) , \( 30 a^{4} - 23 a^{3} - 184 a^{2} - 52 a + 60\) , \( 61 a^{4} - 47 a^{3} - 373 a^{2} - 105 a + 114\bigr] \) |
${y}^2+\left(4a^{4}-3a^{3}-24a^{2}-9a+7\right){x}{y}+\left(2a^{4}-2a^{3}-12a^{2}-a+4\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(30a^{4}-23a^{3}-184a^{2}-52a+60\right){x}+61a^{4}-47a^{3}-373a^{2}-105a+114$ |
| 7.1-d1 |
7.1-d |
$2$ |
$2$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$38.35175$ |
$(-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1736.539102$ |
1.22881840 |
\( \frac{6806591653728}{7} a^{4} - \frac{12152913795431}{7} a^{3} - \frac{25948183338436}{7} a^{2} + 784242424707 a + \frac{3812137965165}{7} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - a + 2\) , \( 3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 6\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 2 a + 3\) , \( -34 a^{4} + 11 a^{3} + 228 a^{2} + 124 a - 104\) , \( -245 a^{4} + 79 a^{3} + 1706 a^{2} + 956 a - 789\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-a+2\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-2a+3\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-19a^{2}-7a+6\right){x}^{2}+\left(-34a^{4}+11a^{3}+228a^{2}+124a-104\right){x}-245a^{4}+79a^{3}+1706a^{2}+956a-789$ |
| 7.1-d2 |
7.1-d |
$2$ |
$2$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$38.35175$ |
$(-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$868.2695511$ |
1.22881840 |
\( \frac{12699246131150107}{7} a^{4} + \frac{30243303793927788}{7} a^{3} + \frac{2913174573201951}{7} a^{2} - \frac{16884080703272684}{7} a + \frac{3651106839935755}{7} \) |
\( \bigl[4 a^{4} - 3 a^{3} - 24 a^{2} - 9 a + 7\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 3 a + 1\) , \( 3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 5\) , \( -21 a^{4} + 16 a^{3} + 88 a^{2} + 43 a - 37\) , \( -131 a^{4} + 31 a^{3} + 1150 a^{2} + 718 a - 568\bigr] \) |
${y}^2+\left(4a^{4}-3a^{3}-24a^{2}-9a+7\right){x}{y}+\left(3a^{4}-3a^{3}-17a^{2}-3a+5\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+3a+1\right){x}^{2}+\left(-21a^{4}+16a^{3}+88a^{2}+43a-37\right){x}-131a^{4}+31a^{3}+1150a^{2}+718a-568$ |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$39.32780$ |
$(-a^4+a^3+6a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$1$ |
$284.5447612$ |
1.61080778 |
\( \frac{44722187}{729} a^{4} - \frac{58908412}{729} a^{3} - \frac{78297241}{243} a^{2} + \frac{13549633}{243} a + \frac{32710483}{729} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - a + 3\) , \( -2 a^{4} + a^{3} + 12 a^{2} + 9 a - 3\) , \( 2 a^{4} - 2 a^{3} - 12 a^{2} - a + 4\) , \( 3 a^{4} - 3 a^{3} - 14 a^{2} - 9 a - 4\) , \( 6 a^{4} + 4 a^{3} - 43 a^{2} - 58 a - 17\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-a+3\right){x}{y}+\left(2a^{4}-2a^{3}-12a^{2}-a+4\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+12a^{2}+9a-3\right){x}^{2}+\left(3a^{4}-3a^{3}-14a^{2}-9a-4\right){x}+6a^{4}+4a^{3}-43a^{2}-58a-17$ |
| 17.1-a1 |
17.1-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$41.91026$ |
$(-a^4+a^3+6a^2+2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.674199578$ |
$480.4143466$ |
4.58392580 |
\( \frac{207138279212}{4913} a^{4} - \frac{64680869328}{4913} a^{3} - \frac{1429821213787}{4913} a^{2} - \frac{796249867220}{4913} a + \frac{663076099367}{4913} \) |
\( \bigl[3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 6\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{4} - a^{3} - 6 a^{2} + 3\) , \( -5 a^{4} + a^{3} + 35 a^{2} + 24 a - 16\) , \( -38 a^{4} + 12 a^{3} + 262 a^{2} + 146 a - 122\bigr] \) |
${y}^2+\left(3a^{4}-2a^{3}-19a^{2}-7a+6\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-5a^{4}+a^{3}+35a^{2}+24a-16\right){x}-38a^{4}+12a^{3}+262a^{2}+146a-122$ |
| 19.1-a1 |
19.1-a |
$2$ |
$3$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$42.37901$ |
$(a^4-a^3-5a^2-3a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$3479.285407$ |
1.09423519 |
\( -\frac{14230}{19} a^{4} + \frac{10518}{19} a^{3} + 4147 a^{2} + \frac{29710}{19} a + \frac{2463}{19} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 3\) , \( 2 a^{4} - 2 a^{3} - 12 a^{2} - a + 4\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 2\) , \( a^{4} + a^{3} - 9 a^{2} - 10 a + 6\) , \( 5 a^{4} - 3 a^{3} - 32 a^{2} - 13 a + 12\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-11a^{2}-3a+3\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-3a+2\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-12a^{2}-a+4\right){x}^{2}+\left(a^{4}+a^{3}-9a^{2}-10a+6\right){x}+5a^{4}-3a^{3}-32a^{2}-13a+12$ |
| 19.1-a2 |
19.1-a |
$2$ |
$3$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$42.37901$ |
$(a^4-a^3-5a^2-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$14.31804694$ |
1.09423519 |
\( -\frac{1435736612114}{6859} a^{4} - \frac{1626171215037}{6859} a^{3} + \frac{75449977659}{361} a^{2} + \frac{1037806706450}{6859} a + \frac{148397329777}{6859} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 3\) , \( 2 a^{4} - 2 a^{3} - 12 a^{2} - a + 4\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 2\) , \( -9 a^{4} + 11 a^{3} + 36 a^{2} - 9\) , \( -77 a^{4} + 61 a^{3} + 425 a^{2} + 155 a - 164\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-11a^{2}-3a+3\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-3a+2\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-12a^{2}-a+4\right){x}^{2}+\left(-9a^{4}+11a^{3}+36a^{2}-9\right){x}-77a^{4}+61a^{3}+425a^{2}+155a-164$ |
| 19.1-b1 |
19.1-b |
$2$ |
$5$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$42.37901$ |
$(a^4-a^3-5a^2-3a+1)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Ns, 5B.1.1 |
$1$ |
\( 1 \) |
$0.307616821$ |
$15814.89119$ |
2.75403475 |
\( -\frac{52270014451}{6859} a^{4} + \frac{74719749282}{6859} a^{3} + \frac{13498969560}{361} a^{2} - \frac{45614115671}{6859} a - \frac{37901982152}{6859} \) |
\( \bigl[3 a^{4} - 2 a^{3} - 18 a^{2} - 9 a + 4\) , \( -2 a^{4} + a^{3} + 12 a^{2} + 8 a - 3\) , \( 2 a^{4} - 2 a^{3} - 12 a^{2} - a + 4\) , \( -5 a^{4} - 5 a^{3} + 23 a^{2} + 31 a\) , \( 9 a^{4} + 22 a^{3} + 19 a^{2} + 12 a\bigr] \) |
${y}^2+\left(3a^{4}-2a^{3}-18a^{2}-9a+4\right){x}{y}+\left(2a^{4}-2a^{3}-12a^{2}-a+4\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+12a^{2}+8a-3\right){x}^{2}+\left(-5a^{4}-5a^{3}+23a^{2}+31a\right){x}+9a^{4}+22a^{3}+19a^{2}+12a$ |
| 19.1-b2 |
19.1-b |
$2$ |
$5$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{15} \) |
$42.37901$ |
$(a^4-a^3-5a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Ns, 5B.1.2 |
$25$ |
\( 1 \) |
$1.538084109$ |
$5.060765180$ |
2.75403475 |
\( -\frac{779035197508243349000563321648160284}{15181127029874798299} a^{4} - \frac{357311188283775399083369648841177493}{15181127029874798299} a^{3} + \frac{278387501860782918364101606759031535}{799006685782884121} a^{2} + \frac{7100222768117184588895064427379272191}{15181127029874798299} a + \frac{1698507796158242983389709903190975873}{15181127029874798299} \) |
\( \bigl[2 a^{4} - a^{3} - 13 a^{2} - 7 a + 4\) , \( -a^{3} + a^{2} + 5 a\) , \( 3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 7\) , \( 78 a^{4} - 91 a^{3} - 411 a^{2} - 24 a + 41\) , \( 292 a^{4} - 334 a^{3} - 1567 a^{2} - 50 a + 97\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-13a^{2}-7a+4\right){x}{y}+\left(3a^{4}-2a^{3}-19a^{2}-7a+7\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(78a^{4}-91a^{3}-411a^{2}-24a+41\right){x}+292a^{4}-334a^{3}-1567a^{2}-50a+97$ |
| 19.1-c1 |
19.1-c |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$42.37901$ |
$(a^4-a^3-5a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.004678740$ |
$16147.65080$ |
1.06923068 |
\( -\frac{67086798}{19} a^{4} + \frac{88149965}{19} a^{3} + 18596197 a^{2} - \frac{61008722}{19} a - \frac{51822334}{19} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} - 2 a\) , \( -a^{4} + a^{3} + 5 a^{2} + 2 a + 1\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - 8 a + 5\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} + a - 1\) , \( -a^{4} - a^{3} + 10 a^{2} + 8 a - 7\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}-2a\right){x}{y}+\left(3a^{4}-2a^{3}-18a^{2}-8a+5\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}+2a+1\right){x}^{2}+\left(-2a^{4}+3a^{3}+9a^{2}+a-1\right){x}-a^{4}-a^{3}+10a^{2}+8a-7$ |
| 19.2-a1 |
19.2-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$42.37901$ |
$(a^4-a^3-5a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.027782377$ |
$7271.128484$ |
2.85893548 |
\( -\frac{10206}{19} a^{4} + \frac{8019}{19} a^{3} + \frac{91854}{19} a^{2} + \frac{58320}{19} a - \frac{39339}{19} \) |
\( \bigl[3 a^{4} - 2 a^{3} - 18 a^{2} - 8 a + 4\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 2 a^{4} - 2 a^{3} - 12 a^{2} - a + 4\) , \( 5 a^{4} - 3 a^{3} - 33 a^{2} - 12 a + 17\) , \( 7 a^{4} - 4 a^{3} - 45 a^{2} - 19 a + 19\bigr] \) |
${y}^2+\left(3a^{4}-2a^{3}-18a^{2}-8a+4\right){x}{y}+\left(2a^{4}-2a^{3}-12a^{2}-a+4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+2\right){x}^{2}+\left(5a^{4}-3a^{3}-33a^{2}-12a+17\right){x}+7a^{4}-4a^{3}-45a^{2}-19a+19$ |
| 19.2-b1 |
19.2-b |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$42.37901$ |
$(a^4-a^3-5a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.124533703$ |
$1315.202087$ |
2.31799518 |
\( -\frac{53376}{19} a^{4} - \frac{96740}{19} a^{3} + \frac{404099}{19} a^{2} + \frac{833279}{19} a + \frac{218732}{19} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 3 a\) , \( 1\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 3 a - 1\) , \( 0\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-11a^{2}-3a+2\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-3a\right){x}^{2}+\left(-2a^{4}+3a^{3}+10a^{2}-3a-1\right){x}$ |
| 21.1-a1 |
21.1-a |
$2$ |
$3$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3 \cdot 7^{3} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$785.3535188$ |
2.22294298 |
\( \frac{470983204}{147} a^{4} - \frac{622087700}{147} a^{3} - \frac{825129042}{49} a^{2} + \frac{21132075}{7} a + \frac{356585129}{147} \) |
\( \bigl[2 a^{4} - a^{3} - 12 a^{2} - 8 a + 3\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 1\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - 9 a + 5\) , \( 8 a^{4} - 10 a^{3} - 43 a^{2} + 7 a + 2\) , \( 40 a^{4} - 53 a^{3} - 210 a^{2} + 40 a + 27\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-12a^{2}-8a+3\right){x}{y}+\left(3a^{4}-2a^{3}-18a^{2}-9a+5\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-1\right){x}^{2}+\left(8a^{4}-10a^{3}-43a^{2}+7a+2\right){x}+40a^{4}-53a^{3}-210a^{2}+40a+27$ |
| 21.1-a2 |
21.1-a |
$2$ |
$3$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{3} \cdot 7^{9} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$261.7845062$ |
2.22294298 |
\( -\frac{54797083360763}{453789} a^{4} - \frac{162193861911353}{453789} a^{3} - \frac{32160526323932}{151263} a^{2} + \frac{294300395939}{3087} a + \frac{18509754926561}{453789} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + 2\) , \( a^{4} - a^{3} - 5 a^{2} - a\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 3\) , \( a^{4} + a^{3} - 8 a^{2} - 9 a - 1\) , \( -8 a^{4} + 16 a^{3} + 28 a^{2} - 13 a - 6\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+2\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-3a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-a\right){x}^{2}+\left(a^{4}+a^{3}-8a^{2}-9a-1\right){x}-8a^{4}+16a^{3}+28a^{2}-13a-6$ |
| 21.1-b1 |
21.1-b |
$8$ |
$12$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{6} \cdot 7^{9} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1343.498707$ |
1.42603981 |
\( -\frac{12076738382337560752}{12252303} a^{4} + \frac{15948359139789204836}{12252303} a^{3} + \frac{21158668459388932445}{4084101} a^{2} - \frac{541191813816259022}{583443} a - \frac{9144991563264350609}{12252303} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 12 a^{2} - a + 4\) , \( a^{3} - 7 a - 2\) , \( a^{4} - 7 a^{2} - 6 a + 2\) , \( -10 a^{4} + 7 a^{3} + 50 a^{2} + 5 a - 4\) , \( 2 a^{4} + 31 a^{3} + 41 a^{2} - 18 a - 9\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-12a^{2}-a+4\right){x}{y}+\left(a^{4}-7a^{2}-6a+2\right){y}={x}^{3}+\left(a^{3}-7a-2\right){x}^{2}+\left(-10a^{4}+7a^{3}+50a^{2}+5a-4\right){x}+2a^{4}+31a^{3}+41a^{2}-18a-9$ |
| 21.1-b2 |
21.1-b |
$8$ |
$12$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{3} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$4030.496122$ |
1.42603981 |
\( \frac{1290782174}{441} a^{4} - \frac{1453652653}{441} a^{3} - \frac{2015496271}{147} a^{2} - \frac{129898778}{21} a - \frac{324119741}{441} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 11 a^{2} - 2 a + 3\) , \( -a^{3} + 2 a^{2} + 5 a - 3\) , \( a^{4} - a^{3} - 6 a^{2} + 3\) , \( 18 a^{4} - 6 a^{3} - 108 a^{2} - 85 a - 22\) , \( -59 a^{4} + 7 a^{3} + 372 a^{2} + 345 a + 70\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-11a^{2}-2a+3\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-3\right){x}^{2}+\left(18a^{4}-6a^{3}-108a^{2}-85a-22\right){x}-59a^{4}+7a^{3}+372a^{2}+345a+70$ |
| 21.1-b3 |
21.1-b |
$8$ |
$12$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{12} \cdot 7^{18} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$335.8746768$ |
1.42603981 |
\( -\frac{6314887039000815116}{21445561257687} a^{4} + \frac{6448190381667455950}{21445561257687} a^{3} + \frac{281328445771073632}{145888171821} a^{2} - \frac{1956433198711976125}{7148520419229} a - \frac{5576392912806486091}{21445561257687} \) |
\( \bigl[1\) , \( 3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 7\) , \( a^{4} - a^{3} - 6 a^{2} + 3\) , \( -174 a^{4} + 59 a^{3} + 1198 a^{2} + 634 a - 587\) , \( -521 a^{4} + 156 a^{3} + 3596 a^{2} + 2073 a - 1585\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-a^{3}-6a^{2}+3\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-19a^{2}-7a+7\right){x}^{2}+\left(-174a^{4}+59a^{3}+1198a^{2}+634a-587\right){x}-521a^{4}+156a^{3}+3596a^{2}+2073a-1585$ |
| 21.1-b4 |
21.1-b |
$8$ |
$12$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{6} \cdot 7^{36} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$10.49608365$ |
1.42603981 |
\( \frac{96174093410263959596416}{1187113512876717321} a^{4} - \frac{29399860877410482942491}{1187113512876717321} a^{3} - \frac{221781997955162712164963}{395704504292239107} a^{2} - \frac{123838860380666162991190}{395704504292239107} a + \frac{44599138991320632660365}{169587644696673903} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 12 a^{2} - a + 4\) , \( a^{3} - 7 a - 2\) , \( a^{4} - 7 a^{2} - 6 a + 2\) , \( -55 a^{4} - 43 a^{3} + 160 a^{2} + 90 a - 64\) , \( 36 a^{4} + 528 a^{3} + 959 a^{2} + 171 a - 333\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-12a^{2}-a+4\right){x}{y}+\left(a^{4}-7a^{2}-6a+2\right){y}={x}^{3}+\left(a^{3}-7a-2\right){x}^{2}+\left(-55a^{4}-43a^{3}+160a^{2}+90a-64\right){x}+36a^{4}+528a^{3}+959a^{2}+171a-333$ |
| 21.1-b5 |
21.1-b |
$8$ |
$12$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{24} \cdot 7^{9} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$83.96866921$ |
1.42603981 |
\( \frac{1847878134868918356056507776}{4746793219636167} a^{4} - \frac{3159815310547261310965358507}{4746793219636167} a^{3} - \frac{2292148882690106367341371763}{1582264406545389} a^{2} + \frac{69067502677402731186886310}{226037772363627} a + \frac{1010370589414902518623031579}{4746793219636167} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + 3\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - 8 a + 5\) , \( 2 a^{4} - a^{3} - 12 a^{2} - 8 a + 2\) , \( -81 a^{4} + 142 a^{3} + 173 a^{2} + 349 a - 209\) , \( -10110 a^{4} + 15971 a^{3} + 45673 a^{2} - 10694 a - 5790\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+3\right){x}{y}+\left(2a^{4}-a^{3}-12a^{2}-8a+2\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-18a^{2}-8a+5\right){x}^{2}+\left(-81a^{4}+142a^{3}+173a^{2}+349a-209\right){x}-10110a^{4}+15971a^{3}+45673a^{2}-10694a-5790$ |
| 21.1-b6 |
21.1-b |
$8$ |
$12$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{6} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1007.624030$ |
1.42603981 |
\( -\frac{159345664472947661}{27783} a^{4} - \frac{73086230158662491}{27783} a^{3} + \frac{360632775784316746}{9261} a^{2} + \frac{484100886595349117}{9261} a + \frac{347423501976218117}{27783} \) |
\( \bigl[4 a^{4} - 3 a^{3} - 24 a^{2} - 9 a + 6\) , \( a^{4} - 7 a^{2} - 7 a + 1\) , \( 3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 4\) , \( 91 a^{4} - 93 a^{3} - 512 a^{2} - 55 a + 77\) , \( 507 a^{4} - 692 a^{3} - 2663 a^{2} + 625 a + 512\bigr] \) |
${y}^2+\left(4a^{4}-3a^{3}-24a^{2}-9a+6\right){x}{y}+\left(3a^{4}-3a^{3}-17a^{2}-3a+4\right){y}={x}^{3}+\left(a^{4}-7a^{2}-7a+1\right){x}^{2}+\left(91a^{4}-93a^{3}-512a^{2}-55a+77\right){x}+507a^{4}-692a^{3}-2663a^{2}+625a+512$ |
| 21.1-b7 |
21.1-b |
$8$ |
$12$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{12} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$31.48825095$ |
1.42603981 |
\( \frac{8163486518210217853471}{1058841} a^{4} - \frac{2550447496916873705996}{1058841} a^{3} - \frac{18782530458125267923718}{352947} a^{2} - \frac{10458909468637893438100}{352947} a + \frac{26129732977890771925085}{1058841} \) |
\( \bigl[4 a^{4} - 3 a^{3} - 24 a^{2} - 9 a + 6\) , \( a^{4} - 7 a^{2} - 7 a + 1\) , \( 3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 4\) , \( 1091 a^{4} - 1418 a^{3} - 5762 a^{2} + 900 a + 827\) , \( 28061 a^{4} - 37099 a^{3} - 147456 a^{2} + 26636 a + 21335\bigr] \) |
${y}^2+\left(4a^{4}-3a^{3}-24a^{2}-9a+6\right){x}{y}+\left(3a^{4}-3a^{3}-17a^{2}-3a+4\right){y}={x}^{3}+\left(a^{4}-7a^{2}-7a+1\right){x}^{2}+\left(1091a^{4}-1418a^{3}-5762a^{2}+900a+827\right){x}+28061a^{4}-37099a^{3}-147456a^{2}+26636a+21335$ |
| 21.1-b8 |
21.1-b |
$8$ |
$12$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7^{3} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$251.9060076$ |
1.42603981 |
\( -\frac{81434005288298314292920127265959}{321489} a^{4} - \frac{37350406360859979041199734878292}{321489} a^{3} + \frac{184302317385055841141700744627670}{107163} a^{2} + \frac{35342836045746069636579502807916}{15309} a + \frac{177548194609305184871145796519643}{321489} \) |
\( \bigl[4 a^{4} - 3 a^{3} - 24 a^{2} - 9 a + 6\) , \( a^{4} - 7 a^{2} - 7 a + 1\) , \( 3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 4\) , \( -29 a^{4} + 272 a^{3} - 62 a^{2} - 1330 a - 353\) , \( 249 a^{4} - 2973 a^{3} + 946 a^{2} + 15222 a + 4653\bigr] \) |
${y}^2+\left(4a^{4}-3a^{3}-24a^{2}-9a+6\right){x}{y}+\left(3a^{4}-3a^{3}-17a^{2}-3a+4\right){y}={x}^{3}+\left(a^{4}-7a^{2}-7a+1\right){x}^{2}+\left(-29a^{4}+272a^{3}-62a^{2}-1330a-353\right){x}+249a^{4}-2973a^{3}+946a^{2}+15222a+4653$ |
| 21.1-c1 |
21.1-c |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{4} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.016840749$ |
$2468.615210$ |
2.35346610 |
\( \frac{10104296}{441} a^{4} + \frac{4664444}{441} a^{3} - \frac{22872250}{147} a^{2} - \frac{30718001}{147} a - \frac{3150614}{63} \) |
\( \bigl[1\) , \( -a^{4} + a^{3} + 7 a^{2} - a - 5\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 2 a + 3\) , \( -3 a^{4} + 5 a^{3} + 13 a^{2} - a + 2\) , \( 6 a^{4} - 11 a^{3} - 20 a^{2} + 7 a\bigr] \) |
${y}^2+{x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+7a^{2}-a-5\right){x}^{2}+\left(-3a^{4}+5a^{3}+13a^{2}-a+2\right){x}+6a^{4}-11a^{3}-20a^{2}+7a$ |
| 21.1-d1 |
21.1-d |
$2$ |
$2$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7 \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$745.6412581$ |
1.05526872 |
\( \frac{2559737498}{45927} a^{4} - \frac{4349236351}{45927} a^{3} - \frac{3325574446}{15309} a^{2} + \frac{43157200}{2187} a + \frac{1097837068}{45927} \) |
\( \bigl[3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 4\) , \( 2 a^{4} - a^{3} - 13 a^{2} - 7 a + 5\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 2 a + 3\) , \( 3 a^{4} + 3 a^{3} - 26 a^{2} - 31 a + 14\) , \( 2 a^{4} + 4 a^{3} - 21 a^{2} - 30 a + 14\bigr] \) |
${y}^2+\left(3a^{4}-3a^{3}-17a^{2}-3a+4\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-2a+3\right){y}={x}^{3}+\left(2a^{4}-a^{3}-13a^{2}-7a+5\right){x}^{2}+\left(3a^{4}+3a^{3}-26a^{2}-31a+14\right){x}+2a^{4}+4a^{3}-21a^{2}-30a+14$ |
| 21.1-d2 |
21.1-d |
$2$ |
$2$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{16} \cdot 7^{2} \) |
$42.80528$ |
$(-a^4+a^3+6a^2+a-1), (-a^4+a^3+6a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$372.8206290$ |
1.05526872 |
\( -\frac{18740710411690571}{301327047} a^{4} - \frac{3499215458689241}{301327047} a^{3} + \frac{40945756677885256}{100442349} a^{2} + \frac{47339501284017344}{100442349} a + \frac{4644632541658694}{43046721} \) |
\( \bigl[3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 4\) , \( 2 a^{4} - a^{3} - 13 a^{2} - 7 a + 5\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 2 a + 3\) , \( 13 a^{4} + 3 a^{3} - 86 a^{2} - 101 a - 21\) , \( 19 a^{4} + 22 a^{3} - 127 a^{2} - 264 a - 136\bigr] \) |
${y}^2+\left(3a^{4}-3a^{3}-17a^{2}-3a+4\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-2a+3\right){y}={x}^{3}+\left(2a^{4}-a^{3}-13a^{2}-7a+5\right){x}^{2}+\left(13a^{4}+3a^{3}-86a^{2}-101a-21\right){x}+19a^{4}+22a^{3}-127a^{2}-264a-136$ |
| 25.1-a1 |
25.1-a |
$2$ |
$2$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$43.55815$ |
$(a^3-a^2-4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.066055937$ |
$12107.90303$ |
2.82978825 |
\( -\frac{315632}{5} a^{4} + 16344 a^{3} + \frac{2177901}{5} a^{2} + \frac{1326764}{5} a - \frac{889488}{5} \) |
\( \bigl[2 a^{4} - a^{3} - 13 a^{2} - 6 a + 5\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a\) , \( 2 a^{4} - 2 a^{3} - 12 a^{2} - a + 5\) , \( -3 a^{4} + 2 a^{3} + 19 a^{2} + 7 a - 7\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a - 2\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-13a^{2}-6a+5\right){x}{y}+\left(2a^{4}-2a^{3}-12a^{2}-a+5\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+4a\right){x}^{2}+\left(-3a^{4}+2a^{3}+19a^{2}+7a-7\right){x}+a^{4}-2a^{3}-4a^{2}+4a-2$ |
| 25.1-a2 |
25.1-a |
$2$ |
$2$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{4} \) |
$43.55815$ |
$(a^3-a^2-4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.132111875$ |
$3026.975758$ |
2.82978825 |
\( \frac{319664488648}{25} a^{4} - \frac{102673678486}{25} a^{3} - \frac{441371263256}{5} a^{2} - \frac{1209469763359}{25} a + \frac{1042758126536}{25} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - a + 2\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( a^{4} - a^{3} - 5 a^{2} - 2 a + 1\) , \( 6 a^{4} - 14 a^{3} - 22 a^{2} + 8 a + 3\) , \( 8 a^{4} - 8 a^{3} - 25 a^{2} + 3 a + 4\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-a+2\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-1\right){x}^{2}+\left(6a^{4}-14a^{3}-22a^{2}+8a+3\right){x}+8a^{4}-8a^{3}-25a^{2}+3a+4$ |
| 25.1-b1 |
25.1-b |
$2$ |
$2$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$43.55815$ |
$(a^3-a^2-4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.018209706$ |
$32742.56756$ |
2.10954515 |
\( 30263 a^{4} - \frac{632587}{5} a^{3} - \frac{96377}{5} a^{2} + \frac{1744654}{5} a + \frac{478868}{5} \) |
\( \bigl[2 a^{4} - a^{3} - 12 a^{2} - 8 a + 3\) , \( a^{4} - 7 a^{2} - 5 a + 2\) , \( 3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 5\) , \( 30 a^{4} + 13 a^{3} - 205 a^{2} - 266 a - 53\) , \( -145 a^{4} - 72 a^{3} + 987 a^{2} + 1355 a + 338\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-12a^{2}-8a+3\right){x}{y}+\left(3a^{4}-3a^{3}-17a^{2}-3a+5\right){y}={x}^{3}+\left(a^{4}-7a^{2}-5a+2\right){x}^{2}+\left(30a^{4}+13a^{3}-205a^{2}-266a-53\right){x}-145a^{4}-72a^{3}+987a^{2}+1355a+338$ |
| 25.1-b2 |
25.1-b |
$2$ |
$2$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{4} \) |
$43.55815$ |
$(a^3-a^2-4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.036419413$ |
$8185.641892$ |
2.10954515 |
\( \frac{657505712651}{25} a^{4} - \frac{1173415723733}{25} a^{3} - \frac{2506810054621}{25} a^{2} + \frac{525774960129}{25} a + \frac{370322397156}{25} \) |
\( \bigl[2 a^{4} - a^{3} - 12 a^{2} - 8 a + 3\) , \( a^{4} - 7 a^{2} - 5 a + 2\) , \( 3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 5\) , \( 45 a^{4} + 18 a^{3} - 305 a^{2} - 391 a - 83\) , \( 30 a^{4} + 12 a^{3} - 204 a^{2} - 260 a - 51\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-12a^{2}-8a+3\right){x}{y}+\left(3a^{4}-3a^{3}-17a^{2}-3a+5\right){y}={x}^{3}+\left(a^{4}-7a^{2}-5a+2\right){x}^{2}+\left(45a^{4}+18a^{3}-305a^{2}-391a-83\right){x}+30a^{4}+12a^{3}-204a^{2}-260a-51$ |
| 27.1-a1 |
27.1-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$43.89467$ |
$(-a^4+a^3+6a^2+a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.092916375$ |
$2905.915841$ |
3.82127616 |
\( 11778 a^{4} - 7825 a^{3} - 72149 a^{2} - 22309 a + 25669 \) |
\( \bigl[3 a^{4} - 2 a^{3} - 18 a^{2} - 8 a + 4\) , \( a^{4} - 8 a^{2} - 4 a + 5\) , \( 3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 6\) , \( 9 a^{4} - 6 a^{3} - 58 a^{2} - 19 a + 26\) , \( 13 a^{4} - 7 a^{3} - 86 a^{2} - 36 a + 38\bigr] \) |
${y}^2+\left(3a^{4}-2a^{3}-18a^{2}-8a+4\right){x}{y}+\left(3a^{4}-2a^{3}-19a^{2}-7a+6\right){y}={x}^{3}+\left(a^{4}-8a^{2}-4a+5\right){x}^{2}+\left(9a^{4}-6a^{3}-58a^{2}-19a+26\right){x}+13a^{4}-7a^{3}-86a^{2}-36a+38$ |
| 27.1-b1 |
27.1-b |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$43.89467$ |
$(-a^4+a^3+6a^2+a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.013832625$ |
$15813.90667$ |
3.09582867 |
\( 11778 a^{4} - 7825 a^{3} - 72149 a^{2} - 22309 a + 25669 \) |
\( \bigl[3 a^{4} - 2 a^{3} - 18 a^{2} - 9 a + 4\) , \( -a^{4} + 6 a^{2} + 8 a + 1\) , \( 0\) , \( -2 a^{4} - 2 a^{3} + 12 a^{2} + 28 a + 18\) , \( -3 a^{4} - 4 a^{3} + 22 a^{2} + 42 a + 17\bigr] \) |
${y}^2+\left(3a^{4}-2a^{3}-18a^{2}-9a+4\right){x}{y}={x}^{3}+\left(-a^{4}+6a^{2}+8a+1\right){x}^{2}+\left(-2a^{4}-2a^{3}+12a^{2}+28a+18\right){x}-3a^{4}-4a^{3}+22a^{2}+42a+17$ |
| 32.1-a1 |
32.1-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{5} \) |
$44.64681$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.023506396$ |
$9247.975180$ |
3.07656325 |
\( \frac{1807}{2} a^{4} - \frac{501}{2} a^{3} - 6172 a^{2} - 3834 a + 2576 \) |
\( \bigl[2 a^{4} - a^{3} - 13 a^{2} - 7 a + 4\) , \( 2 a^{4} - a^{3} - 12 a^{2} - 7 a + 3\) , \( 2 a^{4} - a^{3} - 12 a^{2} - 8 a + 3\) , \( 3 a^{4} + 3 a^{3} - 25 a^{2} - 29 a + 16\) , \( -5 a^{4} + 16 a^{3} + 12 a^{2} - 47 a + 15\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-13a^{2}-7a+4\right){x}{y}+\left(2a^{4}-a^{3}-12a^{2}-8a+3\right){y}={x}^{3}+\left(2a^{4}-a^{3}-12a^{2}-7a+3\right){x}^{2}+\left(3a^{4}+3a^{3}-25a^{2}-29a+16\right){x}-5a^{4}+16a^{3}+12a^{2}-47a+15$ |
| 32.1-b1 |
32.1-b |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( - 2^{5} \) |
$44.64681$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.028895229$ |
$9513.996927$ |
3.89065106 |
\( -\frac{17599}{2} a^{4} - 11045 a^{3} + 35022 a^{2} + \frac{107895}{2} a + \frac{26365}{2} \) |
\( \bigl[1\) , \( -2 a^{4} + a^{3} + 12 a^{2} + 9 a - 2\) , \( 3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 7\) , \( -3 a^{4} + 2 a^{3} + 19 a^{2} + 5 a\) , \( -4 a^{4} + a^{3} + 27 a^{2} + 19 a - 12\bigr] \) |
${y}^2+{x}{y}+\left(3a^{4}-2a^{3}-19a^{2}-7a+7\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+12a^{2}+9a-2\right){x}^{2}+\left(-3a^{4}+2a^{3}+19a^{2}+5a\right){x}-4a^{4}+a^{3}+27a^{2}+19a-12$ |
| 33.1-a1 |
33.1-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{2} \cdot 11 \) |
$44.78441$ |
$(-a^4+a^3+6a^2+a-1), (a^3-a^2-6a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$390.1534008$ |
2.20865825 |
\( \frac{368136379}{99} a^{4} + \frac{172212274}{99} a^{3} - \frac{835200308}{33} a^{2} - \frac{1121916031}{33} a - \frac{805228381}{99} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + 3\) , \( 2 a^{4} - a^{3} - 12 a^{2} - 7 a + 1\) , \( a^{4} - a^{3} - 6 a^{2} + 3\) , \( 3 a + 2\) , \( a^{3} - a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+3\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+3\right){y}={x}^{3}+\left(2a^{4}-a^{3}-12a^{2}-7a+1\right){x}^{2}+\left(3a+2\right){x}+a^{3}-a^{2}-3a-1$ |
| 33.1-b1 |
33.1-b |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{5} \cdot 11^{7} \) |
$44.78441$ |
$(-a^4+a^3+6a^2+a-1), (a^3-a^2-6a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \cdot 7 \) |
$0.004867005$ |
$1561.174439$ |
3.76369529 |
\( -\frac{17692123384}{3557763} a^{4} + \frac{4357009970}{3557763} a^{3} + \frac{40618297175}{1185921} a^{2} + \frac{23104705777}{1185921} a - \frac{57046209614}{3557763} \) |
\( \bigl[3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 4\) , \( -2 a^{4} + a^{3} + 12 a^{2} + 9 a - 2\) , \( 2 a^{4} - 2 a^{3} - 12 a^{2} - a + 4\) , \( -7 a^{4} + 3 a^{3} + 46 a^{2} + 23 a - 11\) , \( 22 a^{4} - 28 a^{3} - 119 a^{2} + 18 a + 26\bigr] \) |
${y}^2+\left(3a^{4}-3a^{3}-17a^{2}-3a+4\right){x}{y}+\left(2a^{4}-2a^{3}-12a^{2}-a+4\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+12a^{2}+9a-2\right){x}^{2}+\left(-7a^{4}+3a^{3}+46a^{2}+23a-11\right){x}+22a^{4}-28a^{3}-119a^{2}+18a+26$ |
| 33.1-c1 |
33.1-c |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{16} \cdot 11^{2} \) |
$44.78441$ |
$(-a^4+a^3+6a^2+a-1), (a^3-a^2-6a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$106.0523502$ |
1.20072463 |
\( -\frac{182675401239074}{473513931} a^{4} + \frac{139309135311595}{473513931} a^{3} + \frac{38597591575826}{14348907} a^{2} + \frac{4216222452883}{14348907} a - \frac{1163023478286790}{473513931} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - a + 2\) , \( a\) , \( 2 a^{4} - a^{3} - 12 a^{2} - 8 a + 2\) , \( 9 a^{4} - 6 a^{3} - 51 a^{2} - 24 a - 6\) , \( -7 a^{4} + 25 a^{3} + 25 a^{2} - 91 a - 33\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-a+2\right){x}{y}+\left(2a^{4}-a^{3}-12a^{2}-8a+2\right){y}={x}^{3}+a{x}^{2}+\left(9a^{4}-6a^{3}-51a^{2}-24a-6\right){x}-7a^{4}+25a^{3}+25a^{2}-91a-33$ |
| 33.1-d1 |
33.1-d |
$2$ |
$3$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{24} \cdot 11^{6} \) |
$44.78441$ |
$(-a^4+a^3+6a^2+a-1), (a^3-a^2-6a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$14.10728336$ |
1.91667182 |
\( -\frac{713310267581100297143}{375913713056211} a^{4} + \frac{1274063225252043947410}{375913713056211} a^{3} + \frac{906148347519768733921}{125304571018737} a^{2} - \frac{192590036519939030914}{125304571018737} a - \frac{399555455632708125403}{375913713056211} \) |
\( \bigl[a^{4} - 7 a^{2} - 6 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} + a + 1\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - 9 a + 5\) , \( -21 a^{4} + 45 a^{3} + 95 a^{2} - 116 a - 46\) , \( -4 a^{4} + 96 a^{3} - 58 a^{2} - 514 a - 154\bigr] \) |
${y}^2+\left(a^{4}-7a^{2}-6a+3\right){x}{y}+\left(3a^{4}-2a^{3}-18a^{2}-9a+5\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}+a+1\right){x}^{2}+\left(-21a^{4}+45a^{3}+95a^{2}-116a-46\right){x}-4a^{4}+96a^{3}-58a^{2}-514a-154$ |
| 33.1-d2 |
33.1-d |
$2$ |
$3$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{8} \cdot 11^{2} \) |
$44.78441$ |
$(-a^4+a^3+6a^2+a-1), (a^3-a^2-6a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{4} \) |
$1$ |
$42.32185008$ |
1.91667182 |
\( -\frac{108440906188451}{72171} a^{4} - \frac{320961085150487}{72171} a^{3} - \frac{63629248263446}{24057} a^{2} + \frac{28552070756006}{24057} a + \frac{3330665774638}{6561} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - a + 2\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 6 a - 3\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 3\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( -7 a^{4} + 13 a^{3} + 23 a^{2} + a - 4\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-a+2\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-3a+3\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+13a^{2}+6a-3\right){x}^{2}+\left(-a^{3}+a^{2}+6a+1\right){x}-7a^{4}+13a^{3}+23a^{2}+a-4$ |
| 33.1-e1 |
33.1-e |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{4} \cdot 11^{2} \) |
$44.78441$ |
$(-a^4+a^3+6a^2+a-1), (a^3-a^2-6a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.010507152$ |
$3758.978334$ |
4.47175489 |
\( -\frac{19668822476}{891} a^{4} + \frac{35117458033}{891} a^{3} + \frac{24993964150}{297} a^{2} - \frac{5287565512}{297} a - \frac{11016331915}{891} \) |
\( \bigl[2 a^{4} - a^{3} - 13 a^{2} - 7 a + 4\) , \( a\) , \( 3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 7\) , \( 2 a^{2} - a - 8\) , \( -9 a^{4} + a^{3} + 61 a^{2} + 49 a - 10\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-13a^{2}-7a+4\right){x}{y}+\left(3a^{4}-2a^{3}-19a^{2}-7a+7\right){y}={x}^{3}+a{x}^{2}+\left(2a^{2}-a-8\right){x}-9a^{4}+a^{3}+61a^{2}+49a-10$ |
| 43.1-a1 |
43.1-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
43.1 |
\( 43 \) |
\( - 43^{2} \) |
$45.98564$ |
$(-a^3+a^2+5a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.041611352$ |
$3247.277761$ |
3.82467383 |
\( -\frac{264338790}{1849} a^{4} + \frac{82355209}{1849} a^{3} + \frac{1824586693}{1849} a^{2} + \frac{1017684605}{1849} a - \frac{844446736}{1849} \) |
\( \bigl[3 a^{4} - 3 a^{3} - 17 a^{2} - 3 a + 5\) , \( -2 a^{4} + 2 a^{3} + 12 a^{2} + a - 4\) , \( 3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 6\) , \( -10 a^{4} + 9 a^{3} + 60 a^{2} + 9 a - 16\) , \( -12 a^{4} + 13 a^{3} + 68 a^{2} + a - 16\bigr] \) |
${y}^2+\left(3a^{4}-3a^{3}-17a^{2}-3a+5\right){x}{y}+\left(3a^{4}-2a^{3}-19a^{2}-7a+6\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+12a^{2}+a-4\right){x}^{2}+\left(-10a^{4}+9a^{3}+60a^{2}+9a-16\right){x}-12a^{4}+13a^{3}+68a^{2}+a-16$ |
| 43.2-a1 |
43.2-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
43.2 |
\( 43 \) |
\( - 43^{2} \) |
$45.98564$ |
$(a^2-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$505.3417653$ |
2.86073954 |
\( -\frac{438416344}{1849} a^{4} + \frac{779169896}{1849} a^{3} + \frac{1664208222}{1849} a^{2} - \frac{328463835}{1849} a - \frac{252084986}{1849} \) |
\( \bigl[4 a^{4} - 3 a^{3} - 24 a^{2} - 9 a + 7\) , \( a^{4} - 7 a^{2} - 5 a + 3\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 2\) , \( a^{4} - 21 a^{3} - 10 a^{2} + 139 a + 148\) , \( 35 a^{4} - 32 a^{3} - 243 a^{2} + 8 a + 250\bigr] \) |
${y}^2+\left(4a^{4}-3a^{3}-24a^{2}-9a+7\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-3a+2\right){y}={x}^{3}+\left(a^{4}-7a^{2}-5a+3\right){x}^{2}+\left(a^{4}-21a^{3}-10a^{2}+139a+148\right){x}+35a^{4}-32a^{3}-243a^{2}+8a+250$ |
| 43.2-b1 |
43.2-b |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
43.2 |
\( 43 \) |
\( 43 \) |
$45.98564$ |
$(a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.320217833$ |
$766.0269305$ |
3.47154411 |
\( -\frac{92854529}{43} a^{4} - \frac{44145619}{43} a^{3} + \frac{631786442}{43} a^{2} + \frac{855090037}{43} a + \frac{205061553}{43} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - a + 3\) , \( -2 a^{4} + a^{3} + 12 a^{2} + 7 a - 1\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 2 a + 2\) , \( 2 a^{4} - 4 a^{3} - 9 a^{2} + 10 a + 2\) , \( 9 a^{4} - 10 a^{3} - 49 a^{2} - 2 a + 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-a+3\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-2a+2\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+12a^{2}+7a-1\right){x}^{2}+\left(2a^{4}-4a^{3}-9a^{2}+10a+2\right){x}+9a^{4}-10a^{3}-49a^{2}-2a+3$ |
| 49.1-a1 |
49.1-a |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{8} \) |
$46.59025$ |
$(-a^4+a^3+6a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$399.5788233$ |
2.26201557 |
\( -\frac{176992}{7} a^{4} - \frac{650231}{7} a^{3} - \frac{527910}{7} a^{2} + \frac{177964}{7} a + \frac{100409}{7} \) |
\( \bigl[3 a^{4} - 2 a^{3} - 18 a^{2} - 9 a + 5\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - 9 a + 5\) , \( 0\) , \( 33 a^{4} - 27 a^{3} - 193 a^{2} - 74 a + 76\) , \( 51 a^{4} - 35 a^{3} - 312 a^{2} - 136 a + 129\bigr] \) |
${y}^2+\left(3a^{4}-2a^{3}-18a^{2}-9a+5\right){x}{y}={x}^{3}+\left(3a^{4}-2a^{3}-18a^{2}-9a+5\right){x}^{2}+\left(33a^{4}-27a^{3}-193a^{2}-74a+76\right){x}+51a^{4}-35a^{3}-312a^{2}-136a+129$ |
| 49.1-b1 |
49.1-b |
$2$ |
$7$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$46.59025$ |
$(-a^4+a^3+6a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$7$ |
7B.1.3 |
$1$ |
\( 3 \) |
$1.806486259$ |
$35.39288654$ |
2.71459494 |
\( -1277575758 a^{4} + 401979083 a^{3} + 8825764361 a^{2} + 4912825548 a - 4092528595 \) |
\( \bigl[2 a^{4} - a^{3} - 13 a^{2} - 7 a + 5\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - 9 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} - 2 a + 1\) , \( 67 a^{4} + 11 a^{3} - 450 a^{2} - 486 a - 46\) , \( 320 a^{4} + 119 a^{3} - 2170 a^{2} - 2735 a - 540\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-13a^{2}-7a+5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}-2a+1\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-18a^{2}-9a+4\right){x}^{2}+\left(67a^{4}+11a^{3}-450a^{2}-486a-46\right){x}+320a^{4}+119a^{3}-2170a^{2}-2735a-540$ |
| 49.1-b2 |
49.1-b |
$2$ |
$7$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$46.59025$ |
$(-a^4+a^3+6a^2+a-3)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$7$ |
7B.1.1 |
$1$ |
\( 3 \) |
$0.258069465$ |
$12139.76008$ |
2.71459494 |
\( 9040 a^{4} + 55632 a^{3} + 44908 a^{2} - 18371 a - 6789 \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + 3\) , \( -a^{3} + 2 a^{2} + 5 a - 3\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} - 3 a + 2\) , \( a + 1\) , \( -3 a^{4} - a^{3} + 20 a^{2} + 26 a + 4\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+3\right){x}{y}+\left(2a^{4}-2a^{3}-11a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-3\right){x}^{2}+\left(a+1\right){x}-3a^{4}-a^{3}+20a^{2}+26a+4$ |
| 49.1-c1 |
49.1-c |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$46.59025$ |
$(-a^4+a^3+6a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$1512.216884$ |
4.28032960 |
\( 516053 a^{4} + 235337 a^{3} - 3338710 a^{2} - 4352787 a - 1032777 \) |
\( \bigl[2 a^{4} - a^{3} - 13 a^{2} - 7 a + 5\) , \( -3 a^{4} + 3 a^{3} + 17 a^{2} + 3 a - 3\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - 8 a + 4\) , \( -3 a^{4} + 4 a^{3} + 16 a^{2} - 2 a - 4\) , \( a^{3} - a^{2} - 5 a - 2\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-13a^{2}-7a+5\right){x}{y}+\left(3a^{4}-2a^{3}-18a^{2}-8a+4\right){y}={x}^{3}+\left(-3a^{4}+3a^{3}+17a^{2}+3a-3\right){x}^{2}+\left(-3a^{4}+4a^{3}+16a^{2}-2a-4\right){x}+a^{3}-a^{2}-5a-2$ |
| 49.1-d1 |
49.1-d |
$1$ |
$1$ |
5.5.124817.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{8} \) |
$46.59025$ |
$(-a^4+a^3+6a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.018851819$ |
$2763.219749$ |
2.21168403 |
\( 516053 a^{4} + 235337 a^{3} - 3338710 a^{2} - 4352787 a - 1032777 \) |
\( \bigl[3 a^{4} - 2 a^{3} - 18 a^{2} - 8 a + 5\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 6 a - 4\) , \( a^{4} - a^{3} - 5 a^{2} - 2 a\) , \( 4 a^{4} - 2 a^{3} - 23 a^{2} - 16 a - 7\) , \( -a^{4} + 5 a^{2} + 8 a + 9\bigr] \) |
${y}^2+\left(3a^{4}-2a^{3}-18a^{2}-8a+5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}-2a\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+13a^{2}+6a-4\right){x}^{2}+\left(4a^{4}-2a^{3}-23a^{2}-16a-7\right){x}-a^{4}+5a^{2}+8a+9$ |
*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.
