| 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 |
| 5.2-a1 |
5.2-a |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{9} \) |
$44.06952$ |
$(-a^2-a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$779.6314072$ |
1.85689169 |
\( -\frac{53530296763371}{1953125} a^{4} + \frac{100014856320409}{1953125} a^{3} + \frac{180804411882303}{1953125} a^{2} - \frac{317603485307297}{1953125} a + \frac{61665020065632}{1953125} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\) , \( a^{2} - 2\) , \( -18 a^{4} + 18 a^{3} + 84 a^{2} - 28 a - 65\) , \( -17 a^{4} + 143 a^{3} - 247 a^{2} - 66 a + 232\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-1\right){x}^{2}+\left(-18a^{4}+18a^{3}+84a^{2}-28a-65\right){x}-17a^{4}+143a^{3}-247a^{2}-66a+232$ |
| 5.2-a2 |
5.2-a |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{3} \) |
$44.06952$ |
$(-a^2-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 3 \) |
$1$ |
$3.208359700$ |
1.85689169 |
\( -\frac{128231881914538928397109901}{125} a^{4} + \frac{239577746439798947952809904}{125} a^{3} + \frac{433130088782320853746714593}{125} a^{2} - \frac{760789667505783079512509382}{125} a + \frac{147678727085673562670583767}{125} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\) , \( a^{2} - 2\) , \( -793 a^{4} + 1613 a^{3} + 1474 a^{2} - 1738 a - 1115\) , \( -24574 a^{4} + 60991 a^{3} + 16792 a^{2} - 57375 a - 8583\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-1\right){x}^{2}+\left(-793a^{4}+1613a^{3}+1474a^{2}-1738a-1115\right){x}-24574a^{4}+60991a^{3}+16792a^{2}-57375a-8583$ |
| 5.2-b1 |
5.2-b |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$44.06952$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.017310315$ |
$10351.90709$ |
2.13399108 |
\( -\frac{166646}{5} a^{4} + \frac{311509}{5} a^{3} + \frac{561358}{5} a^{2} - \frac{989857}{5} a + \frac{200902}{5} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{4} + 4 a^{2} + a + 1\) , \( 1\) , \( -16 a^{4} + 9 a^{3} + 86 a^{2} - 21 a - 66\) , \( -7 a^{4} + 3 a^{3} + 39 a^{2} - 7 a - 29\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+4a^{2}+a+1\right){x}^{2}+\left(-16a^{4}+9a^{3}+86a^{2}-21a-66\right){x}-7a^{4}+3a^{3}+39a^{2}-7a-29$ |
| 5.2-c1 |
5.2-c |
$2$ |
$7$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{7} \) |
$44.06952$ |
$(-a^2-a+1)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$4703.086268$ |
1.60022906 |
\( -\frac{301659126}{78125} a^{4} + \frac{2149173679}{78125} a^{3} - \frac{3430026607}{78125} a^{2} - \frac{1209241707}{78125} a + \frac{3262696342}{78125} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( a\) , \( 2 a^{2} + a - 1\) , \( a^{4} - 3 a^{2} + a\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}^{2}+\left(2a^{2}+a-1\right){x}+a^{4}-3a^{2}+a$ |
| 5.2-c2 |
5.2-c |
$2$ |
$7$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$44.06952$ |
$(-a^2-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.279829015$ |
1.60022906 |
\( -\frac{351193178427896632381}{5} a^{4} + \frac{664359810180196274169}{5} a^{3} + \frac{1180608811554262654718}{5} a^{2} - \frac{2118022921751973620162}{5} a + \frac{412443982986116998527}{5} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( a\) , \( 850 a^{4} - 1415 a^{3} - 2913 a^{2} + 4276 a - 1146\) , \( 24875 a^{4} - 44425 a^{3} - 84869 a^{2} + 138741 a - 29175\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}^{2}+\left(850a^{4}-1415a^{3}-2913a^{2}+4276a-1146\right){x}+24875a^{4}-44425a^{3}-84869a^{2}+138741a-29175$ |
| 5.2-d1 |
5.2-d |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$44.06952$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.098799873$ |
$1857.844653$ |
2.18591384 |
\( \frac{16904862}{5} a^{4} - \frac{31790583}{5} a^{3} - \frac{56884456}{5} a^{2} + \frac{101504769}{5} a - \frac{20860074}{5} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( a^{2} + a - 1\) , \( -7 a^{4} + 5 a^{3} + 37 a^{2} - 12 a - 32\) , \( -15 a^{4} + 11 a^{3} + 77 a^{2} - 27 a - 66\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-7a^{4}+5a^{3}+37a^{2}-12a-32\right){x}-15a^{4}+11a^{3}+77a^{2}-27a-66$ |
| 5.2-e1 |
5.2-e |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{3} \) |
$44.06952$ |
$(-a^2-a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.668968791$ |
$3256.276059$ |
2.88238385 |
\( -\frac{841247181}{125} a^{4} - \frac{1103140726}{125} a^{3} + \frac{1652051008}{125} a^{2} + \frac{1295199408}{125} a - \frac{361984598}{125} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 3 a^{4} + 2 a^{3} - 4 a^{2} + 5 a - 2\) , \( 8 a^{4} + 8 a^{3} - 20 a^{2} - 11 a + 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+3a-2\right){x}^{2}+\left(3a^{4}+2a^{3}-4a^{2}+5a-2\right){x}+8a^{4}+8a^{3}-20a^{2}-11a+3$ |
| 5.2-e2 |
5.2-e |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{9} \) |
$44.06952$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$2.006906375$ |
$13.40031300$ |
2.88238385 |
\( -\frac{3693478091042515836}{1953125} a^{4} + \frac{7258220761664669769}{1953125} a^{3} + \frac{11143725442178482298}{1953125} a^{2} - \frac{20649972819777975677}{1953125} a + \frac{4031638378702696787}{1953125} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{2} + a + 3\) , \( a^{4} - 4 a^{2} + 1\) , \( -1383 a^{4} + 1069 a^{3} + 7153 a^{2} - 2527 a - 6098\) , \( -43797 a^{4} + 33879 a^{3} + 226668 a^{2} - 80047 a - 193337\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-1383a^{4}+1069a^{3}+7153a^{2}-2527a-6098\right){x}-43797a^{4}+33879a^{3}+226668a^{2}-80047a-193337$ |
| 23.1-a1 |
23.1-a |
$4$ |
$6$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{6} \) |
$51.33506$ |
$(a^4-4a^2+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$2.690240220$ |
$1827.761124$ |
3.25315865 |
\( -\frac{2294727771000760176805232}{148035889} a^{4} - \frac{423651906747301577131905}{148035889} a^{3} + \frac{10971772468806027048005013}{148035889} a^{2} + \frac{6113194277922661332551040}{148035889} a - \frac{1937100834773343253045615}{148035889} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -8 a^{4} + 18 a^{3} + 15 a^{2} - 24 a - 14\) , \( -8 a^{4} + 34 a^{3} - 27 a^{2} - 22 a + 27\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a\right){x}^{2}+\left(-8a^{4}+18a^{3}+15a^{2}-24a-14\right){x}-8a^{4}+34a^{3}-27a^{2}-22a+27$ |
| 23.1-a2 |
23.1-a |
$4$ |
$6$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{3} \) |
$51.33506$ |
$(a^4-4a^2+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1.345120110$ |
$7311.044499$ |
3.25315865 |
\( -\frac{584364299885}{12167} a^{4} - \frac{105658091790}{12167} a^{3} + \frac{2792663360247}{12167} a^{2} + \frac{1547131747555}{12167} a - \frac{491068265928}{12167} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -3 a^{4} + 8 a^{3} - 9 a + 1\) , \( 7 a^{4} - 18 a^{3} + 16 a - 3\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a\right){x}^{2}+\left(-3a^{4}+8a^{3}-9a+1\right){x}+7a^{4}-18a^{3}+16a-3$ |
| 23.1-a3 |
23.1-a |
$4$ |
$6$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{18} \) |
$51.33506$ |
$(a^4-4a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$8.070720662$ |
$7.521650719$ |
3.25315865 |
\( -\frac{136215886955938924281570626693030}{3244150909895248285300369} a^{4} + \frac{142371791822936664730647373224707}{3244150909895248285300369} a^{3} + \frac{876467995697100940868632282890011}{3244150909895248285300369} a^{2} - \frac{1201482936627101406973475516279393}{3244150909895248285300369} a + \frac{226435476306702683225249646070491}{3244150909895248285300369} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -378 a^{4} + 978 a^{3} + 145 a^{2} - 889 a - 39\) , \( -12495 a^{4} + 34988 a^{3} - 2115 a^{2} - 30288 a + 5294\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a\right){x}^{2}+\left(-378a^{4}+978a^{3}+145a^{2}-889a-39\right){x}-12495a^{4}+34988a^{3}-2115a^{2}-30288a+5294$ |
| 23.1-a4 |
23.1-a |
$4$ |
$6$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{9} \) |
$51.33506$ |
$(a^4-4a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$4.035360331$ |
$30.08660287$ |
3.25315865 |
\( -\frac{75095661844366326647104517743}{1801152661463} a^{4} + \frac{140302467400985233974487084292}{1801152661463} a^{3} + \frac{253651355623849449478889525090}{1801152661463} a^{2} - \frac{445536654010793337505121437983}{1801152661463} a + \frac{86484200225845707305075413308}{1801152661463} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 6 a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( 50 a^{4} + 18 a^{3} - 245 a^{2} - 174 a + 36\) , \( -111 a^{4} + 27 a^{3} + 542 a^{2} + 72 a - 249\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-6a+2\right){x}^{2}+\left(50a^{4}+18a^{3}-245a^{2}-174a+36\right){x}-111a^{4}+27a^{3}+542a^{2}+72a-249$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{2} \) |
$51.33506$ |
$(a^4-4a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$317.8742060$ |
1.51419752 |
\( \frac{38434427725432397}{529} a^{4} - \frac{104249077305109274}{529} a^{3} - \frac{2990826886270049}{529} a^{2} + \frac{92382965215245991}{529} a - \frac{7626992326510379}{529} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( -4 a^{4} + 9 a^{3} + 25 a^{2} - 29 a - 39\) , \( -51 a^{4} - 6 a^{3} + 239 a^{2} + 33 a - 199\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a-1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){x}^{2}+\left(-4a^{4}+9a^{3}+25a^{2}-29a-39\right){x}-51a^{4}-6a^{3}+239a^{2}+33a-199$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$51.33506$ |
$(a^4-4a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2542.993648$ |
1.51419752 |
\( -\frac{179898692}{23} a^{4} - \frac{122487899}{23} a^{3} + \frac{1057739840}{23} a^{2} + \frac{559114286}{23} a - \frac{288758325}{23} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 14 a^{4} + 12 a^{3} - 70 a^{2} - 49 a + 15\) , \( -44 a^{4} - 23 a^{3} + 256 a^{2} + 157 a - 49\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-2a\right){x}^{2}+\left(14a^{4}+12a^{3}-70a^{2}-49a+15\right){x}-44a^{4}-23a^{3}+256a^{2}+157a-49$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{5} \) |
$51.76489$ |
$(-a^4+a^3+4a^2-2a-1), (-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.262890012$ |
$367.8812747$ |
2.30345121 |
\( \frac{23653157}{625} a^{4} + \frac{4359119}{625} a^{3} - \frac{113099368}{625} a^{2} - \frac{62979578}{625} a + \frac{20023799}{625} \) |
\( \bigl[a + 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 4 a + 3\) , \( 1\) , \( -a^{4} + a^{3} + 6 a^{2} - 7 a + 3\) , \( -2 a^{4} + 4 a^{3} + 4 a^{2} - 8 a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-4a+3\right){x}^{2}+\left(-a^{4}+a^{3}+6a^{2}-7a+3\right){x}-2a^{4}+4a^{3}+4a^{2}-8a+2$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{7} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.041060736$ |
$3672.511789$ |
3.59159352 |
\( \frac{16904862}{5} a^{4} - \frac{31790583}{5} a^{3} - \frac{56884456}{5} a^{2} + \frac{101504769}{5} a - \frac{20860074}{5} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a^{4} - 5 a^{2} - a + 2\) , \( -46 a^{4} + 34 a^{3} + 238 a^{2} - 80 a - 200\) , \( 267 a^{4} - 205 a^{3} - 1380 a^{2} + 483 a + 1175\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(-46a^{4}+34a^{3}+238a^{2}-80a-200\right){x}+267a^{4}-205a^{3}-1380a^{2}+483a+1175$ |
| 25.2-b1 |
25.2-b |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{7} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.013985660$ |
$3027.433459$ |
2.01690214 |
\( -\frac{166646}{5} a^{4} + \frac{311509}{5} a^{3} + \frac{561358}{5} a^{2} - \frac{989857}{5} a + \frac{200902}{5} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( a\) , \( -2 a^{3} + 3 a^{2} + 4 a - 1\) , \( a^{4} - 2 a^{3} - a^{2}\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}^{2}+\left(-2a^{3}+3a^{2}+4a-1\right){x}+a^{4}-2a^{3}-a^{2}$ |
| 25.2-c1 |
25.2-c |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{15} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.303412060$ |
$378.7249576$ |
2.73686901 |
\( -\frac{53530296763371}{1953125} a^{4} + \frac{100014856320409}{1953125} a^{3} + \frac{180804411882303}{1953125} a^{2} - \frac{317603485307297}{1953125} a + \frac{61665020065632}{1953125} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( a^{4} - 5 a^{2} - a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( 15 a^{4} + 4 a^{3} - 68 a^{2} - 39 a + 9\) , \( 245 a^{4} + 47 a^{3} - 1167 a^{2} - 653 a + 202\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+2\right){x}^{2}+\left(15a^{4}+4a^{3}-68a^{2}-39a+9\right){x}+245a^{4}+47a^{3}-1167a^{2}-653a+202$ |
| 25.2-c2 |
25.2-c |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{9} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.910236180$ |
$126.2416525$ |
2.73686901 |
\( -\frac{128231881914538928397109901}{125} a^{4} + \frac{239577746439798947952809904}{125} a^{3} + \frac{433130088782320853746714593}{125} a^{2} - \frac{760789667505783079512509382}{125} a + \frac{147678727085673562670583767}{125} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( a^{4} - 5 a^{2} - a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -120 a^{4} - 41 a^{3} + 602 a^{2} + 411 a - 201\) , \( -6241 a^{4} - 1409 a^{3} + 29986 a^{2} + 17683 a - 5288\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+2\right){x}^{2}+\left(-120a^{4}-41a^{3}+602a^{2}+411a-201\right){x}-6241a^{4}-1409a^{3}+29986a^{2}+17683a-5288$ |
| 25.2-d1 |
25.2-d |
$2$ |
$7$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{13} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \) |
$0.310780859$ |
$505.0480580$ |
3.73838664 |
\( -\frac{301659126}{78125} a^{4} + \frac{2149173679}{78125} a^{3} - \frac{3430026607}{78125} a^{2} - \frac{1209241707}{78125} a + \frac{3262696342}{78125} \) |
\( \bigl[a^{4} - 4 a^{2} - a\) , \( -a^{4} + 5 a^{2} - 3\) , \( a^{4} - 4 a^{2}\) , \( -4 a^{4} + a^{3} + 20 a^{2} - 2 a - 17\) , \( -11 a^{4} + 53 a^{2} + 17 a - 21\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a\right){x}{y}+\left(a^{4}-4a^{2}\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-3\right){x}^{2}+\left(-4a^{4}+a^{3}+20a^{2}-2a-17\right){x}-11a^{4}+53a^{2}+17a-21$ |
| 25.2-d2 |
25.2-d |
$2$ |
$7$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{7} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B.6.3 |
$1$ |
\( 2 \) |
$2.175466015$ |
$72.14972257$ |
3.73838664 |
\( -\frac{351193178427896632381}{5} a^{4} + \frac{664359810180196274169}{5} a^{3} + \frac{1180608811554262654718}{5} a^{2} - \frac{2118022921751973620162}{5} a + \frac{412443982986116998527}{5} \) |
\( \bigl[a^{3} - 3 a - 1\) , \( -a^{3} + 4 a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( 4134 a^{4} - 8264 a^{3} - 13178 a^{2} + 26471 a - 7308\) , \( 324353 a^{4} - 597283 a^{3} - 1109011 a^{2} + 1892257 a - 331085\bigr] \) |
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(4134a^{4}-8264a^{3}-13178a^{2}+26471a-7308\right){x}+324353a^{4}-597283a^{3}-1109011a^{2}+1892257a-331085$ |
| 25.2-e1 |
25.2-e |
$2$ |
$5$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$51.76489$ |
$(-a^2-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.2 |
$1$ |
\( 3 \) |
$1$ |
$373.3141428$ |
2.66742947 |
\( -18265196557302123882 a^{4} - 23976105726198776372 a^{3} + 35877254141910486033 a^{2} + 28176522533483407877 a - 7897895856558777768 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 5 a + 1\) , \( a^{3} - 3 a - 1\) , \( 225 a^{4} - 21 a^{3} - 1051 a^{2} - 334 a + 214\) , \( -2140 a^{4} - 899 a^{3} + 10386 a^{2} + 7903 a - 1482\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-5a+1\right){x}^{2}+\left(225a^{4}-21a^{3}-1051a^{2}-334a+214\right){x}-2140a^{4}-899a^{3}+10386a^{2}+7903a-1482$ |
| 25.2-e2 |
25.2-e |
$2$ |
$5$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$51.76489$ |
$(-a^2-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.1 |
$1$ |
\( 3 \) |
$1$ |
$373.3141428$ |
2.66742947 |
\( -2363080 a^{4} - 424465 a^{3} + 11302411 a^{2} + 6237194 a - 2040382 \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a\) , \( a^{4} - 5 a^{2} + 3\) , \( -a^{2} - 2 a\) , \( -37 a^{4} + 105 a^{3} - 10 a^{2} - 91 a + 18\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a\right){x}^{2}+\left(-a^{2}-2a\right){x}-37a^{4}+105a^{3}-10a^{2}-91a+18$ |
| 25.2-f1 |
25.2-f |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$51.76489$ |
$(-a^2-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$1152.006196$ |
2.74379754 |
\( -4102 a^{4} + 3029 a^{3} + 21367 a^{2} - 6455 a - 17568 \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( a^{4} - 4 a^{2}\) , \( a^{4} - a^{3} - 6 a^{2} + 3\) , \( -2 a^{2}\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{4}-4a^{2}\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){x}^{2}+\left(a^{4}-a^{3}-6a^{2}+3\right){x}-2a^{2}$ |
| 25.2-g1 |
25.2-g |
$2$ |
$5$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$9.148463548$ |
$1.566761868$ |
4.26735149 |
\( -18265196557302123882 a^{4} - 23976105726198776372 a^{3} + 35877254141910486033 a^{2} + 28176522533483407877 a - 7897895856558777768 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{4} - 4 a^{2} - 2 a + 1\) , \( a^{4} - 4 a^{2} - a + 1\) , \( 44 a^{4} + 35 a^{3} - 302 a^{2} - 86 a + 145\) , \( -296 a^{4} + 783 a^{3} + 551 a^{2} - 1379 a - 942\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{4}-4a^{2}-a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}-2a+1\right){x}^{2}+\left(44a^{4}+35a^{3}-302a^{2}-86a+145\right){x}-296a^{4}+783a^{3}+551a^{2}-1379a-942$ |
| 25.2-g2 |
25.2-g |
$2$ |
$5$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1.829692709$ |
$4896.130840$ |
4.26735149 |
\( -2363080 a^{4} - 424465 a^{3} + 11302411 a^{2} + 6237194 a - 2040382 \) |
\( \bigl[a^{3} - 2 a - 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 2\) , \( a^{3} - 3 a\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 8 a + 6\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 7 a\bigr] \) |
${y}^2+\left(a^{3}-2a-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+2\right){x}^{2}+\left(2a^{4}+a^{3}-9a^{2}-8a+6\right){x}+a^{4}-2a^{3}-2a^{2}+7a$ |
| 25.2-h1 |
25.2-h |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{9} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.168355982$ |
$601.8296148$ |
4.82646710 |
\( -\frac{841247181}{125} a^{4} - \frac{1103140726}{125} a^{3} + \frac{1652051008}{125} a^{2} + \frac{1295199408}{125} a - \frac{361984598}{125} \) |
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( -a^{4} + 5 a^{2} - 3\) , \( a^{4} - 5 a^{2} - a + 2\) , \( -7 a^{4} + 18 a^{3} + 2 a^{2} - 16 a\) , \( 25 a^{4} - 71 a^{3} + 7 a^{2} + 60 a - 14\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-3\right){x}^{2}+\left(-7a^{4}+18a^{3}+2a^{2}-16a\right){x}+25a^{4}-71a^{3}+7a^{2}+60a-14$ |
| 25.2-h2 |
25.2-h |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{15} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.505067946$ |
$200.6098716$ |
4.82646710 |
\( -\frac{3693478091042515836}{1953125} a^{4} + \frac{7258220761664669769}{1953125} a^{3} + \frac{11143725442178482298}{1953125} a^{2} - \frac{20649972819777975677}{1953125} a + \frac{4031638378702696787}{1953125} \) |
\( \bigl[a^{4} - 4 a^{2} - a\) , \( a^{3} - 4 a - 1\) , \( 1\) , \( 494 a^{4} - 951 a^{3} - 1621 a^{2} + 3036 a - 718\) , \( 12705 a^{4} - 23606 a^{3} - 43160 a^{2} + 74867 a - 13895\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(494a^{4}-951a^{3}-1621a^{2}+3036a-718\right){x}+12705a^{4}-23606a^{3}-43160a^{2}+74867a-13895$ |
| 25.2-i1 |
25.2-i |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$51.76489$ |
$(-a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.023633444$ |
$13245.42969$ |
3.72786624 |
\( -4102 a^{4} + 3029 a^{3} + 21367 a^{2} - 6455 a - 17568 \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( a^{4} - 6 a^{2} - a + 4\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){y}={x}^{3}+\left(a^{4}-6a^{2}-a+4\right){x}^{2}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){x}+a^{4}-2a^{3}-3a^{2}+4a+1$ |
| 25.3-a1 |
25.3-a |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{2} \) |
$51.76489$ |
$(-a^4+a^3+4a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.041684839$ |
$8481.371657$ |
4.21028481 |
\( 1515 a^{4} - 2960 a^{3} - 4865 a^{2} + 9341 a - 578 \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( a + 1\) , \( -a^{3} + a^{2} + 3 a + 1\) , \( -a\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}^{2}+\left(-a^{3}+a^{2}+3a+1\right){x}-a$ |
| 25.3-b1 |
25.3-b |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{8} \) |
$51.76489$ |
$(-a^4+a^3+4a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$1299.873435$ |
3.09598121 |
\( 1515 a^{4} - 2960 a^{3} - 4865 a^{2} + 9341 a - 578 \) |
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a + 1\) , \( a^{2} - 2\) , \( 4 a^{4} + 5 a^{3} - 7 a^{2} - 7 a + 7\) , \( 9 a^{4} + 15 a^{3} - 15 a^{2} - 17 a + 2\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-4a+1\right){x}^{2}+\left(4a^{4}+5a^{3}-7a^{2}-7a+7\right){x}+9a^{4}+15a^{3}-15a^{2}-17a+2$ |
| 25.3-c1 |
25.3-c |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{8} \) |
$51.76489$ |
$(-a^4+a^3+4a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$207.3270835$ |
1.48140750 |
\( 14676551511 a^{4} - 27418949334 a^{3} - 49572515642 a^{2} + 87071232017 a - 16901541561 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 3 a + 2\) , \( a + 1\) , \( 33 a^{4} + 12 a^{3} - 163 a^{2} - 114 a + 34\) , \( -195 a^{4} - 33 a^{3} + 930 a^{2} + 506 a - 162\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-3a+2\right){x}^{2}+\left(33a^{4}+12a^{3}-163a^{2}-114a+34\right){x}-195a^{4}-33a^{3}+930a^{2}+506a-162$ |
| 25.3-d1 |
25.3-d |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{2} \) |
$51.76489$ |
$(-a^4+a^3+4a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.037323194$ |
$9811.982631$ |
4.36116816 |
\( 14676551511 a^{4} - 27418949334 a^{3} - 49572515642 a^{2} + 87071232017 a - 16901541561 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 4 a\) , \( a^{4} - 4 a^{2} - a + 1\) , \( -13 a^{4} + 12 a^{3} + 69 a^{2} - 29 a - 60\) , \( -63 a^{4} + 51 a^{3} + 329 a^{2} - 120 a - 283\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{4}-4a^{2}-a+1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-13a^{4}+12a^{3}+69a^{2}-29a-60\right){x}-63a^{4}+51a^{3}+329a^{2}-120a-283$ |
| 25.3-e1 |
25.3-e |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{8} \) |
$51.76489$ |
$(-a^4+a^3+4a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$762.2323940$ |
1.81545149 |
\( 18715158 a^{4} + 24479609 a^{3} - 36978980 a^{2} - 28962235 a + 8120144 \) |
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 2 a^{4} - a^{3} - 2 a^{2} + 7 a - 9\) , \( -31 a^{4} + 59 a^{3} + 114 a^{2} - 180 a + 16\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){x}^{2}+\left(2a^{4}-a^{3}-2a^{2}+7a-9\right){x}-31a^{4}+59a^{3}+114a^{2}-180a+16$ |
| 25.3-f1 |
25.3-f |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{2} \) |
$51.76489$ |
$(-a^4+a^3+4a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.795226170$ |
$279.9161133$ |
2.65085404 |
\( 18715158 a^{4} + 24479609 a^{3} - 36978980 a^{2} - 28962235 a + 8120144 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( -3 a^{4} + 8 a^{3} + 3 a^{2} - 12 a + 1\) , \( -3 a^{4} + 11 a^{3} - 4 a^{2} - 11 a + 2\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-1\right){x}^{2}+\left(-3a^{4}+8a^{3}+3a^{2}-12a+1\right){x}-3a^{4}+11a^{3}-4a^{2}-11a+2$ |
| 31.1-a1 |
31.1-a |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( 31 \) |
$52.89048$ |
$(-a^4+a^3+5a^2-2a-2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 1 \) |
$1$ |
$605.2084978$ |
5.06947420 |
\( \frac{1750660261}{31} a^{4} - \frac{3270957006}{31} a^{3} - \frac{5913170024}{31} a^{2} + \frac{10387522347}{31} a - \frac{2016617989}{31} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( a^{3} - 2 a\) , \( 8 a^{4} - 15 a^{3} - 26 a^{2} + 44 a - 9\) , \( 16 a^{4} - 32 a^{3} - 54 a^{2} + 100 a - 21\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a\right){x}^{2}+\left(8a^{4}-15a^{3}-26a^{2}+44a-9\right){x}+16a^{4}-32a^{3}-54a^{2}+100a-21$ |
| 32.1-a1 |
32.1-a |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{5} \) |
$53.05866$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.029576870$ |
$12274.76805$ |
4.32347313 |
\( \frac{14339}{2} a^{4} - \frac{10233}{2} a^{3} - 36243 a^{2} + 11068 a + 29508 \) |
\( \bigl[a + 1\) , \( a^{4} - 6 a^{2} - a + 5\) , \( 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{4}-6a^{2}-a+5\right){x}^{2}+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){x}$ |
| 35.2-a1 |
35.2-a |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( - 5^{7} \cdot 7 \) |
$53.53627$ |
$(-a^4+a^3+4a^2-2a-1), (a^2-2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 7 \) |
$1$ |
$45.41011551$ |
5.32387482 |
\( \frac{730325952287753}{546875} a^{4} - \frac{1365139303552274}{546875} a^{3} - \frac{353224339385121}{78125} a^{2} + \frac{4359330548268313}{546875} a - \frac{863192448685554}{546875} \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -110 a^{4} + 92 a^{3} + 588 a^{2} - 210 a - 509\) , \( -1057 a^{4} + 814 a^{3} + 5470 a^{2} - 1924 a - 4668\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(-110a^{4}+92a^{3}+588a^{2}-210a-509\right){x}-1057a^{4}+814a^{3}+5470a^{2}-1924a-4668$ |
| 35.2-b1 |
35.2-b |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( - 5^{5} \cdot 7^{3} \) |
$53.53627$ |
$(-a^4+a^3+4a^2-2a-1), (a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.071850761$ |
$4647.328514$ |
3.97650929 |
\( -\frac{5392833849}{153125} a^{4} - \frac{3946327208}{153125} a^{3} + \frac{1271140618}{21875} a^{2} + \frac{5319407046}{153125} a - \frac{1607939593}{153125} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( -13 a^{4} + 11 a^{3} + 70 a^{2} - 24 a - 59\) , \( -258 a^{4} + 201 a^{3} + 1339 a^{2} - 472 a - 1144\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-13a^{4}+11a^{3}+70a^{2}-24a-59\right){x}-258a^{4}+201a^{3}+1339a^{2}-472a-1144$ |
| 35.2-c1 |
35.2-c |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7 \) |
$53.53627$ |
$(-a^4+a^3+4a^2-2a-1), (a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.040265461$ |
$6941.856794$ |
3.32870710 |
\( -\frac{4711274}{35} a^{4} + \frac{15190172}{35} a^{3} - \frac{1101237}{5} a^{2} - \frac{5769914}{35} a + \frac{1515617}{35} \) |
\( \bigl[a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 2\) , \( a^{3} - 3 a\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - a + 1\) , \( a^{4} - 2 a^{3} - a^{2} + 2 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-2a-2\right){x}^{2}+\left(-a^{4}+2a^{3}+2a^{2}-a+1\right){x}+a^{4}-2a^{3}-a^{2}+2a$ |
| 47.1-a1 |
47.1-a |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( 47 \) |
$55.13801$ |
$(a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.030480532$ |
$11721.77805$ |
4.25484059 |
\( \frac{482704689}{47} a^{4} - \frac{373345106}{47} a^{3} - \frac{2498103323}{47} a^{2} + \frac{882159448}{47} a + \frac{2130648757}{47} \) |
\( \bigl[a^{4} - 4 a^{2}\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a\) , \( a^{3} - 3 a\) , \( a^{4} + 4 a^{3} - 2 a^{2} - 12 a + 3\) , \( a^{4} + 6 a^{3} + a^{2} - 10 a + 2\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-5a\right){x}^{2}+\left(a^{4}+4a^{3}-2a^{2}-12a+3\right){x}+a^{4}+6a^{3}+a^{2}-10a+2$ |
| 47.1-b1 |
47.1-b |
$1$ |
$1$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( 47 \) |
$55.13801$ |
$(a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.160443053$ |
$2786.687710$ |
5.32447109 |
\( \frac{5699208916}{47} a^{4} + \frac{1051537638}{47} a^{3} - \frac{27249295617}{47} a^{2} - \frac{15180036213}{47} a + \frac{4810909510}{47} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 4 a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -a^{4} + 5 a^{2} - 6 a + 1\) , \( 4 a^{3} - a^{2} - 6 a + 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-4a+2\right){x}^{2}+\left(-a^{4}+5a^{2}-6a+1\right){x}+4a^{3}-a^{2}-6a+1$ |
| 47.1-c1 |
47.1-c |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( 47^{3} \) |
$55.13801$ |
$(a^2-a-4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.922976668$ |
$3569.458596$ |
4.35931060 |
\( -\frac{1082686075331}{103823} a^{4} + \frac{3093018738461}{103823} a^{3} - \frac{325859428923}{103823} a^{2} - \frac{2649966013829}{103823} a + \frac{584346836528}{103823} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 2 a - 1\) , \( -2 a^{4} + 2 a^{3} + 3 a^{2} + 5 a - 1\) , \( -a^{4} - 2 a^{3} + 12 a^{2} - 9 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-2a^{4}+2a^{3}+3a^{2}+5a-1\right){x}-a^{4}-2a^{3}+12a^{2}-9a+1$ |
| 47.1-c2 |
47.1-c |
$2$ |
$3$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( 47^{9} \) |
$55.13801$ |
$(a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$2.768930004$ |
$14.68913002$ |
4.35931060 |
\( \frac{2374796432115434012945423888}{1119130473102767} a^{4} + \frac{438433486127119263446234579}{1119130473102767} a^{3} - \frac{11354604706047593476152148984}{1119130473102767} a^{2} - \frac{6326495422193928336814201516}{1119130473102767} a + \frac{2004693521561629984625819738}{1119130473102767} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 2 a - 1\) , \( -7 a^{4} + 22 a^{3} + 18 a^{2} - 75 a - 1\) , \( 42 a^{4} - 26 a^{3} - 157 a^{2} - 13 a - 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-7a^{4}+22a^{3}+18a^{2}-75a-1\right){x}+42a^{4}-26a^{3}-157a^{2}-13a-20$ |
| 47.1-d1 |
47.1-d |
$2$ |
$2$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( -47 \) |
$55.13801$ |
$(a^2-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2483.687230$ |
1.47888417 |
\( \frac{228119}{47} a^{4} - \frac{281938}{47} a^{3} - \frac{885367}{47} a^{2} + \frac{719658}{47} a + \frac{5303}{47} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{4} - 4 a^{2} + 1\) , \( -8 a^{4} + 25 a^{3} - 3 a^{2} - 24 a + 5\) , \( 19 a^{4} - 53 a^{3} + 4 a^{2} + 45 a - 10\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}^{2}+\left(-8a^{4}+25a^{3}-3a^{2}-24a+5\right){x}+19a^{4}-53a^{3}+4a^{2}+45a-10$ |
| 47.1-d2 |
47.1-d |
$2$ |
$2$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{2} \) |
$55.13801$ |
$(a^2-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1241.843615$ |
1.47888417 |
\( -\frac{171847551504}{2209} a^{4} + \frac{262684239756}{2209} a^{3} + \frac{621583453235}{2209} a^{2} - \frac{776701606461}{2209} a + \frac{141459947097}{2209} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{2} + a - 2\) , \( 12 a^{4} - 31 a^{3} - 44 a^{2} + 87 a - 14\) , \( 47 a^{4} - 79 a^{3} - 153 a^{2} + 256 a - 50\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}^{2}+\left(12a^{4}-31a^{3}-44a^{2}+87a-14\right){x}+47a^{4}-79a^{3}-153a^{2}+256a-50$ |
| 55.1-a1 |
55.1-a |
$2$ |
$2$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{22} \cdot 11^{2} \) |
$56.01155$ |
$(-a^4+a^3+4a^2-2a-1), (a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.802984477$ |
$483.1453928$ |
4.62010924 |
\( \frac{6114574394311674565556}{288486480712890625} a^{4} + \frac{8282274291898467293802}{288486480712890625} a^{3} - \frac{11400713698933294492894}{288486480712890625} a^{2} - \frac{9271207824794399809824}{288486480712890625} a + \frac{3020532854658394192367}{288486480712890625} \) |
\( \bigl[a^{3} - 2 a - 1\) , \( a^{4} - 4 a^{2} - a + 1\) , \( a^{2} - 1\) , \( 10 a^{4} + 11 a^{3} - 55 a^{2} - 27 a + 19\) , \( 10 a^{4} + 32 a^{3} - 70 a^{2} - 60 a + 16\bigr] \) |
${y}^2+\left(a^{3}-2a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-4a^{2}-a+1\right){x}^{2}+\left(10a^{4}+11a^{3}-55a^{2}-27a+19\right){x}+10a^{4}+32a^{3}-70a^{2}-60a+16$ |
| 55.1-a2 |
55.1-a |
$2$ |
$2$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{11} \cdot 11 \) |
$56.01155$ |
$(-a^4+a^3+4a^2-2a-1), (a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.401492238$ |
$3865.163143$ |
4.62010924 |
\( -\frac{10563907950892}{537109375} a^{4} + \frac{18399886785636}{537109375} a^{3} + \frac{36570206952008}{537109375} a^{2} - \frac{57032096975732}{537109375} a + \frac{11889908446931}{537109375} \) |
\( \bigl[a^{3} - 2 a - 1\) , \( a^{4} - 4 a^{2} - a + 1\) , \( a^{2} - 1\) , \( 5 a^{4} + a^{3} - 10 a^{2} - 7 a - 1\) , \( a^{4} + 5 a^{3} + 16 a^{2} + 6 a - 4\bigr] \) |
${y}^2+\left(a^{3}-2a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-4a^{2}-a+1\right){x}^{2}+\left(5a^{4}+a^{3}-10a^{2}-7a-1\right){x}+a^{4}+5a^{3}+16a^{2}+6a-4$ |
| 55.1-b1 |
55.1-b |
$4$ |
$6$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11^{2} \) |
$56.01155$ |
$(-a^4+a^3+4a^2-2a-1), (a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2^{2} \) |
$2.758936195$ |
$2.112029148$ |
5.62074438 |
\( -\frac{7699847142216262321659066149}{3025} a^{4} - \frac{1421543315366012932838560058}{3025} a^{3} + \frac{36815247523744416910876960376}{3025} a^{2} + \frac{20512525313681941527923735896}{3025} a - \frac{6499847395985803829390692518}{3025} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( -a^{4} + 6 a^{2} - 4\) , \( a^{3} - 3 a - 1\) , \( -460 a^{4} + 318 a^{3} + 2321 a^{2} - 688 a - 2066\) , \( -7726 a^{4} + 5705 a^{3} + 39394 a^{2} - 13083 a - 34058\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-4\right){x}^{2}+\left(-460a^{4}+318a^{3}+2321a^{2}-688a-2066\right){x}-7726a^{4}+5705a^{3}+39394a^{2}-13083a-34058$ |
| 55.1-b2 |
55.1-b |
$4$ |
$6$ |
5.5.176281.1 |
$5$ |
$[5, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{6} \cdot 11^{6} \) |
$56.01155$ |
$(-a^4+a^3+4a^2-2a-1), (a^3-3a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.919645398$ |
$513.2230830$ |
5.62074438 |
\( -\frac{1059706128554445034}{27680640625} a^{4} - \frac{193964844425988978}{27680640625} a^{3} + \frac{5067248063580948266}{27680640625} a^{2} + \frac{2812338334195999661}{27680640625} a - \frac{892169117477952638}{27680640625} \) |
\( \bigl[a^{3} - 2 a - 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 3\) , \( a^{4} - 5 a^{2} + 3\) , \( -4 a^{4} + 9 a^{3} + 24 a^{2} - 27 a - 33\) , \( -77 a^{4} + 67 a^{3} + 405 a^{2} - 165 a - 361\bigr] \) |
${y}^2+\left(a^{3}-2a-1\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-6a-3\right){x}^{2}+\left(-4a^{4}+9a^{3}+24a^{2}-27a-33\right){x}-77a^{4}+67a^{3}+405a^{2}-165a-361$ |
*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.
