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 |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.94441$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$53.30948644$ |
1.03787 |
\( 7023555026985694166784 a^{5} - 9648887366434646044480 a^{4} - 28885788338374354679552 a^{3} + 25635887672503641709056 a^{2} + 13946567436683584709504 a - 5112540269534105084096 \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a\) , \( a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -5 a^{4} + a^{3} + 25 a^{2} - 9 a - 40\) , \( -5 a^{5} - 12 a^{4} + 25 a^{3} + 58 a^{2} - 41 a - 85\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a^{4}+a^{3}+25a^{2}-9a-40\right){x}-5a^{5}-12a^{4}+25a^{3}+58a^{2}-41a-85$ |
1.1-a2 |
1.1-a |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.94441$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$38862.61561$ |
1.03787 |
\( 7229184 a^{5} - 9936448 a^{4} - 29730048 a^{3} + 26409216 a^{2} + 14360192 a - 5264576 \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a\) , \( a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( a^{3} - 4 a\) , \( -a^{5} + 5 a^{3} + 2 a^{2} - 4 a - 3\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{3}-4a\right){x}-a^{5}+5a^{3}+2a^{2}-4a-3$ |
1.1-a3 |
1.1-a |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.94441$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$38862.61561$ |
1.03787 |
\( -677120 a^{5} + 1182464 a^{4} + 2016384 a^{3} - 2159296 a^{2} - 1004032 a + 393856 \) |
\( \bigl[a^{4} - 5 a^{2} - a + 4\) , \( a^{4} - 5 a^{2} - a + 2\) , \( a\) , \( a + 3\) , \( -1\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+4\right){x}{y}+a{y}={x}^{3}+\left(a^{4}-5a^{2}-a+2\right){x}^{2}+\left(a+3\right){x}-1$ |
1.1-a4 |
1.1-a |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.94441$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$53.30948644$ |
1.03787 |
\( 12308760270848 a^{5} + 28874105852416 a^{4} - 6662502842752 a^{3} - 40744939056320 a^{2} - 8372520666624 a + 5331447389056 \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 12 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 4 a + 1\) , \( a^{4} - 5 a^{2} - a + 3\) , \( -162 a^{5} - 60 a^{4} + 974 a^{3} + 654 a^{2} - 983 a - 652\) , \( -2114 a^{5} - 652 a^{4} + 12586 a^{3} + 7999 a^{2} - 12759 a - 8028\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+12a+1\right){x}{y}+\left(a^{4}-5a^{2}-a+3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-4a+1\right){x}^{2}+\left(-162a^{5}-60a^{4}+974a^{3}+654a^{2}-983a-652\right){x}-2114a^{5}-652a^{4}+12586a^{3}+7999a^{2}-12759a-8028$ |
1.1-b1 |
1.1-b |
$4$ |
$10$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.94441$ |
$\textsf{none}$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$107233.3560$ |
1.03097 |
\( -143104 a^{5} - 19008 a^{4} + 591872 a^{3} + 549888 a^{2} + 47488 a - 66240 \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a\) , \( -a^{5} + 6 a^{3} + 2 a^{2} - 8 a - 3\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 5 a + 2\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 5 a + 3\) , \( -5 a^{5} - 2 a^{4} + 29 a^{3} + 19 a^{2} - 29 a - 18\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+5a+2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+2a^{2}-8a-3\right){x}^{2}+\left(a^{5}-5a^{3}-2a^{2}+5a+3\right){x}-5a^{5}-2a^{4}+29a^{3}+19a^{2}-29a-18$ |
1.1-b2 |
1.1-b |
$4$ |
$10$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.94441$ |
$\textsf{none}$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$107233.3560$ |
1.03097 |
\( -74805248 a^{5} + 44483840 a^{4} + 422387584 a^{3} - 101569472 a^{2} - 463288576 a + 125886336 \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 4 a + 4\) , \( -a^{5} + a^{4} + 4 a^{3} - a^{2} - 2 a\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 8 a + 3\) , \( -a^{5} + 5 a^{3} + 3 a^{2} - 5 a - 2\) , \( -a - 1\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+4a+4\right){x}{y}+\left(a^{5}-6a^{3}-2a^{2}+8a+3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-a^{2}-2a\right){x}^{2}+\left(-a^{5}+5a^{3}+3a^{2}-5a-2\right){x}-a-1$ |
1.1-b3 |
1.1-b |
$4$ |
$10$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.94441$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$6.862934784$ |
1.03097 |
\( 43947467566485424618752 a^{5} + 102582202153948218381248 a^{4} - 24237374604196736331264 a^{3} - 144469827819074580106240 a^{2} - 29589275923062683993728 a + 18827631547255305666368 \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a - 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 3 a - 1\) , \( 1\) , \( -35 a^{5} + 43 a^{4} + 248 a^{3} - 160 a^{2} - 470 a - 30\) , \( 2361 a^{5} - 1116 a^{4} - 13035 a^{3} + 1768 a^{2} + 12754 a - 4101\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-3a-1\right){x}^{2}+\left(-35a^{5}+43a^{4}+248a^{3}-160a^{2}-470a-30\right){x}+2361a^{5}-1116a^{4}-13035a^{3}+1768a^{2}+12754a-4101$ |
1.1-b4 |
1.1-b |
$4$ |
$10$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.94441$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$6.862934784$ |
1.03097 |
\( 118396285564667127487488 a^{5} + 32464855447295289493760 a^{4} - 701475687166178787181184 a^{3} - 429140723558121836462528 a^{2} + 711101459746538007506176 a + 431780158684442992128896 \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 4 a + 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 8 a^{2} - 6 a + 4\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 5 a + 2\) , \( 254 a^{5} - 282 a^{4} - 1334 a^{3} + 998 a^{2} + 1451 a - 1099\) , \( 4022 a^{5} - 3924 a^{4} - 21915 a^{3} + 13762 a^{2} + 24444 a - 15555\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+4a+4\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+5a+2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-8a^{2}-6a+4\right){x}^{2}+\left(254a^{5}-282a^{4}-1334a^{3}+998a^{2}+1451a-1099\right){x}+4022a^{5}-3924a^{4}-21915a^{3}+13762a^{2}+24444a-15555$ |
17.1-a1 |
17.1-a |
$1$ |
$1$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$117.69573$ |
$(a^2-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1952.305692$ |
1.87699 |
\( \frac{1689894763}{17} a^{5} - \frac{1004776218}{17} a^{4} - \frac{9542047412}{17} a^{3} + \frac{2293708361}{17} a^{2} + \frac{10465955183}{17} a - \frac{2842982358}{17} \) |
\( \bigl[a^{5} - 5 a^{3} - 2 a^{2} + 4 a + 1\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 5 a + 2\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 4 a + 2\) , \( a^{5} + a^{4} - 3 a^{3} - 2 a^{2} + 2 a + 1\) , \( -a^{5} + 4 a^{4} + 8 a^{3} - 7 a^{2} - 6 a\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-2a^{2}+4a+1\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+4a+2\right){y}={x}^{3}+\left(a^{5}-5a^{3}-2a^{2}+5a+2\right){x}^{2}+\left(a^{5}+a^{4}-3a^{3}-2a^{2}+2a+1\right){x}-a^{5}+4a^{4}+8a^{3}-7a^{2}-6a$ |
17.1-b1 |
17.1-b |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$117.69573$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.006916699$ |
$145742.7834$ |
2.90752 |
\( -\frac{185481856}{289} a^{5} + \frac{102497984}{289} a^{4} + \frac{1044555392}{289} a^{3} - \frac{213653952}{289} a^{2} - \frac{1119092608}{289} a + \frac{302023552}{289} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 4\) , \( a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a\) , \( a^{5} - 6 a^{3} - a^{2} + 8 a\) , \( 2 a^{5} - a^{4} - 10 a^{3} + 2 a^{2} + 9 a - 2\) , \( -a^{5} + a^{4} + 6 a^{3} - 2 a^{2} - 6 a + 2\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+4\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+8a\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a\right){x}^{2}+\left(2a^{5}-a^{4}-10a^{3}+2a^{2}+9a-2\right){x}-a^{5}+a^{4}+6a^{3}-2a^{2}-6a+2$ |
17.1-b2 |
17.1-b |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$117.69573$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.013833399$ |
$145742.7834$ |
2.90752 |
\( -\frac{206778624}{17} a^{5} + \frac{361969152}{17} a^{4} + \frac{607889280}{17} a^{3} - \frac{653178304}{17} a^{2} - \frac{302978176}{17} a + \frac{117945792}{17} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 7 a + 1\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 4 a^{2} + 8 a - 1\) , \( -a^{5} + 4 a^{3} + 2 a^{2} + 1\) , \( a^{5} - a^{4} - 4 a^{3} + a^{2} + 2 a - 2\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+7a+1\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+4a^{2}+8a-1\right){y}={x}^{3}+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){x}^{2}+\left(-a^{5}+4a^{3}+2a^{2}+1\right){x}+a^{5}-a^{4}-4a^{3}+a^{2}+2a-2$ |
17.1-c1 |
17.1-c |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17^{18} \) |
$117.69573$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \) |
$1$ |
$24.78970731$ |
0.965254 |
\( \frac{970532289405115296885008992012707712}{14063084452067724991009} a^{5} - \frac{1688412998994237453435420512416795712}{14063084452067724991009} a^{4} - \frac{2885899957267596885430497880233769088}{14063084452067724991009} a^{3} + \frac{3079470082017783334281531315872956224}{14063084452067724991009} a^{2} + \frac{1436441810530492014545159255107542144}{14063084452067724991009} a - \frac{557880640280580636178787340246723968}{14063084452067724991009} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 4 a^{2} + 7 a - 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 2\) , \( 1\) , \( 13 a^{5} + 23 a^{4} - 37 a^{3} - 85 a^{2} - 28 a\) , \( -42 a^{5} - 115 a^{4} - 72 a^{3} + 28 a^{2} + 66 a + 13\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+4a^{2}+7a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-2\right){x}^{2}+\left(13a^{5}+23a^{4}-37a^{3}-85a^{2}-28a\right){x}-42a^{5}-115a^{4}-72a^{3}+28a^{2}+66a+13$ |
17.1-c2 |
17.1-c |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$117.69573$ |
$(a^2-a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$36143.39326$ |
0.965254 |
\( -\frac{6494202087424}{4913} a^{5} + \frac{8283221178624}{4913} a^{4} + \frac{26345210904960}{4913} a^{3} - \frac{15815126171072}{4913} a^{2} - \frac{22029013295744}{4913} a + \frac{6648918922944}{4913} \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 4 a + 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 7 a - 4\) , \( a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a\) , \( 4 a^{5} + 14 a^{4} - 57 a^{3} - 43 a^{2} + 121 a - 27\) , \( -73 a^{5} - 18 a^{4} + 532 a^{3} + 81 a^{2} - 780 a + 198\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+4a+4\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+7a-4\right){x}^{2}+\left(4a^{5}+14a^{4}-57a^{3}-43a^{2}+121a-27\right){x}-73a^{5}-18a^{4}+532a^{3}+81a^{2}-780a+198$ |
17.1-c3 |
17.1-c |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$117.69573$ |
$(a^2-a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$18071.69663$ |
0.965254 |
\( \frac{112886477726418816}{24137569} a^{5} + \frac{30920004961346240}{24137569} a^{4} - \frac{668876982773454464}{24137569} a^{3} - \frac{409020354035048896}{24137569} a^{2} + \frac{678294548723282816}{24137569} a + \frac{411799115647905408}{24137569} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a\) , \( a^{5} - 7 a^{3} - a^{2} + 11 a + 2\) , \( 2 a^{5} - a^{4} - 10 a^{3} + 10 a + 1\) , \( a^{5} + 3 a^{4} - 14 a^{3} - 8 a^{2} + 33 a - 7\) , \( -9 a^{5} - 5 a^{4} + 69 a^{3} + 19 a^{2} - 103 a + 23\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a\right){x}{y}+\left(2a^{5}-a^{4}-10a^{3}+10a+1\right){y}={x}^{3}+\left(a^{5}-7a^{3}-a^{2}+11a+2\right){x}^{2}+\left(a^{5}+3a^{4}-14a^{3}-8a^{2}+33a-7\right){x}-9a^{5}-5a^{4}+69a^{3}+19a^{2}-103a+23$ |
17.1-c4 |
17.1-c |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17^{9} \) |
$117.69573$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$49.57941462$ |
0.965254 |
\( -\frac{5512623245294523779795205904329704049408}{118587876497} a^{5} + \frac{9590185576993242271164940433148348352256}{118587876497} a^{4} + \frac{16391911227260398226700599822270494514048}{118587876497} a^{3} - \frac{17491389534775214528047295733728779447488}{118587876497} a^{2} - \frac{8158989227560729933090578011644295389056}{118587876497} a + \frac{3168761939024878259498372983372720103872}{118587876497} \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 4 a + 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 7 a - 4\) , \( a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a\) , \( -a^{5} + 19 a^{4} - 27 a^{3} - 83 a^{2} + 131 a - 22\) , \( -214 a^{5} + 180 a^{4} + 1134 a^{3} - 563 a^{2} - 929 a + 284\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+4a+4\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+7a-4\right){x}^{2}+\left(-a^{5}+19a^{4}-27a^{3}-83a^{2}+131a-22\right){x}-214a^{5}+180a^{4}+1134a^{3}-563a^{2}-929a+284$ |
17.1-d1 |
17.1-d |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$117.69573$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.006091408$ |
$127792.6373$ |
2.24523 |
\( \frac{3137152}{289} a^{5} - \frac{620352}{289} a^{4} - \frac{18575232}{289} a^{3} - \frac{4943296}{289} a^{2} + \frac{22294144}{289} a + \frac{12110208}{289} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 4 a + 1\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 5 a^{2} + 11 a - 1\) , \( a^{5} - 6 a^{3} + 5 a - 1\) , \( a^{5} - 6 a^{3} - a^{2} + 5 a - 2\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a\right){x}{y}+\left(2a^{5}-2a^{4}-10a^{3}+5a^{2}+11a-1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+4a+1\right){x}^{2}+\left(a^{5}-6a^{3}+5a-1\right){x}+a^{5}-6a^{3}-a^{2}+5a-2$ |
17.1-d2 |
17.1-d |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$117.69573$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.012182817$ |
$127792.6373$ |
2.24523 |
\( -\frac{10479872}{17} a^{5} + \frac{6423040}{17} a^{4} + \frac{59572864}{17} a^{3} - \frac{14498240}{17} a^{2} - \frac{65494144}{17} a + \frac{17800640}{17} \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 4 a + 4\) , \( -a^{5} + 6 a^{3} + 2 a^{2} - 8 a - 3\) , \( a^{5} - 5 a^{3} - 3 a^{2} + 5 a + 3\) , \( 86 a^{5} - 54 a^{4} - 484 a^{3} + 130 a^{2} + 532 a - 155\) , \( -567 a^{5} + 336 a^{4} + 3203 a^{3} - 766 a^{2} - 3514 a + 951\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+4a+4\right){x}{y}+\left(a^{5}-5a^{3}-3a^{2}+5a+3\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+2a^{2}-8a-3\right){x}^{2}+\left(86a^{5}-54a^{4}-484a^{3}+130a^{2}+532a-155\right){x}-567a^{5}+336a^{4}+3203a^{3}-766a^{2}-3514a+951$ |
23.1-a1 |
23.1-a |
$1$ |
$1$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{5} \) |
$120.69815$ |
$(2a^5-a^4-10a^3+8a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1581.723567$ |
1.52071 |
\( -\frac{8456762167111}{6436343} a^{5} + \frac{13474539884077}{6436343} a^{4} + \frac{1497269279108}{279841} a^{3} - \frac{39346254495760}{6436343} a^{2} - \frac{19272482884676}{6436343} a + \frac{7385865765984}{6436343} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 8 a\) , \( -a^{5} + 6 a^{3} + a^{2} - 6 a - 1\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 7 a + 2\) , \( 8343 a^{5} - 4960 a^{4} - 47109 a^{3} + 11324 a^{2} + 51671 a - 14038\) , \( -89193 a^{5} + 53027 a^{4} + 503633 a^{3} - 121032 a^{2} - 552394 a + 150021\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+8a\right){x}{y}+\left(a^{5}-6a^{3}-2a^{2}+7a+2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-6a-1\right){x}^{2}+\left(8343a^{5}-4960a^{4}-47109a^{3}+11324a^{2}+51671a-14038\right){x}-89193a^{5}+53027a^{4}+503633a^{3}-121032a^{2}-552394a+150021$ |
23.1-b1 |
23.1-b |
$1$ |
$1$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$120.69815$ |
$(2a^5-a^4-10a^3+8a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.007486460$ |
$62411.72215$ |
2.69531 |
\( -\frac{2467147}{23} a^{5} + \frac{1333589}{23} a^{4} + 620653 a^{3} - \frac{3176311}{23} a^{2} - \frac{15924489}{23} a + \frac{4307659}{23} \) |
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 2 a^{2} + 14 a - 2\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 4 a^{2} + 8 a\) , \( -a^{5} - a^{4} + 8 a^{3} + 3 a^{2} - 12 a + 4\) , \( -2 a^{5} + a^{4} + 12 a^{3} - 3 a^{2} - 14 a + 4\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+4a^{2}+8a\right){y}={x}^{3}+\left(2a^{5}-a^{4}-12a^{3}+2a^{2}+14a-2\right){x}^{2}+\left(-a^{5}-a^{4}+8a^{3}+3a^{2}-12a+4\right){x}-2a^{5}+a^{4}+12a^{3}-3a^{2}-14a+4$ |
25.1-a1 |
25.1-a |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$121.53973$ |
$(-a^5+5a^3+3a^2-4a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.172205993$ |
$5453.779711$ |
2.70883 |
\( -\frac{13234177536}{25} a^{5} + \frac{23027347904}{25} a^{4} + \frac{39338336256}{25} a^{3} - \frac{41983480576}{25} a^{2} - \frac{19581655424}{25} a + \frac{1520871744}{5} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 4\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 5 a^{2} + 10 a - 2\) , \( -20 a^{5} + 25 a^{4} + 85 a^{3} - 65 a^{2} - 48 a + 15\) , \( -57 a^{5} + 79 a^{4} + 232 a^{3} - 211 a^{2} - 108 a + 40\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+4\right){x}{y}+\left(2a^{5}-2a^{4}-10a^{3}+5a^{2}+10a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(-20a^{5}+25a^{4}+85a^{3}-65a^{2}-48a+15\right){x}-57a^{5}+79a^{4}+232a^{3}-211a^{2}-108a+40$ |
25.1-a2 |
25.1-a |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$121.53973$ |
$(-a^5+5a^3+3a^2-4a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.086102996$ |
$5453.779711$ |
2.70883 |
\( \frac{209401250304}{625} a^{5} + \frac{57428760576}{625} a^{4} - \frac{1240676953472}{625} a^{3} - \frac{759032698048}{625} a^{2} + \frac{1257708985088}{625} a + \frac{763688663168}{625} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -6 a^{5} + 8 a^{4} + 24 a^{3} - 18 a^{2} - 15 a + 4\) , \( -11 a^{5} + 15 a^{4} + 44 a^{3} - 37 a^{2} - 22 a + 6\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a-1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){x}^{2}+\left(-6a^{5}+8a^{4}+24a^{3}-18a^{2}-15a+4\right){x}-11a^{5}+15a^{4}+44a^{3}-37a^{2}-22a+6$ |
31.1-a1 |
31.1-a |
$4$ |
$4$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$123.73809$ |
$(a^3-4a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$19008.02851$ |
1.14217 |
\( \frac{3796546}{31} a^{5} - \frac{6627622}{31} a^{4} - \frac{11240934}{31} a^{3} + \frac{12144135}{31} a^{2} + \frac{5513216}{31} a - \frac{2213100}{31} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 12 a\) , \( a - 1\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 4 a + 1\) , \( -a^{5} - a^{4} + 5 a^{3} + 4 a^{2} - 5 a - 1\) , \( -a^{5} - a^{4} + 3 a^{3} + a^{2} - 3 a\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+12a\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+4a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a^{5}-a^{4}+5a^{3}+4a^{2}-5a-1\right){x}-a^{5}-a^{4}+3a^{3}+a^{2}-3a$ |
31.1-a2 |
31.1-a |
$4$ |
$4$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$123.73809$ |
$(a^3-4a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$2376.003564$ |
1.14217 |
\( -\frac{140958617561466}{961} a^{5} + \frac{245225564532027}{961} a^{4} + \frac{419141274676586}{961} a^{3} - \frac{447266158603579}{961} a^{2} - \frac{208622584206982}{961} a + \frac{81030514885376}{961} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 7 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 9 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 6 a + 1\) , \( -7 a^{5} + 12 a^{4} + 49 a^{3} - 42 a^{2} - 107 a - 21\) , \( 49 a^{5} + 43 a^{4} - 263 a^{3} - 316 a^{2} + 101 a + 133\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+7a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+6a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-9a+2\right){x}^{2}+\left(-7a^{5}+12a^{4}+49a^{3}-42a^{2}-107a-21\right){x}+49a^{5}+43a^{4}-263a^{3}-316a^{2}+101a+133$ |
31.1-a3 |
31.1-a |
$4$ |
$4$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31 \) |
$123.73809$ |
$(a^3-4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$297.0004455$ |
1.14217 |
\( \frac{406151423066717}{31} a^{5} + \frac{567068890292162}{31} a^{4} - \frac{1218810555829845}{31} a^{3} - \frac{1399755737003582}{31} a^{2} + \frac{962921986534943}{31} a + \frac{772142086205712}{31} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + a^{2} + 3 a + 1\) , \( a^{4} - 4 a^{2} + 1\) , \( 2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 12 a + 1\) , \( 789 a^{5} - 457 a^{4} - 4482 a^{3} + 1033 a^{2} + 4975 a - 1360\) , \( 17362 a^{5} - 10291 a^{4} - 98107 a^{3} + 23419 a^{2} + 107776 a - 29258\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+a^{2}+3a+1\right){x}{y}+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+12a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}+1\right){x}^{2}+\left(789a^{5}-457a^{4}-4482a^{3}+1033a^{2}+4975a-1360\right){x}+17362a^{5}-10291a^{4}-98107a^{3}+23419a^{2}+107776a-29258$ |
31.1-a4 |
31.1-a |
$4$ |
$4$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{4} \) |
$123.73809$ |
$(a^3-4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$37.12505569$ |
1.14217 |
\( -\frac{193932318407885499187632358531}{923521} a^{5} + \frac{337379653959790603073371254530}{923521} a^{4} + \frac{576662181684976760836577195403}{923521} a^{3} - \frac{615341476047697763847893079806}{923521} a^{2} - \frac{287030625232085428934780062081}{923521} a + \frac{111476029101446214094810159328}{923521} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 6 a + 1\) , \( a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 8 a - 1\) , \( 1\) , \( 195 a^{5} - 148 a^{4} - 1069 a^{3} + 400 a^{2} + 1171 a - 436\) , \( 12048 a^{5} - 7182 a^{4} - 67921 a^{3} + 16246 a^{2} + 74403 a - 20017\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+6a+1\right){x}{y}+{y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+3a^{2}+8a-1\right){x}^{2}+\left(195a^{5}-148a^{4}-1069a^{3}+400a^{2}+1171a-436\right){x}+12048a^{5}-7182a^{4}-67921a^{3}+16246a^{2}+74403a-20017$ |
31.1-b1 |
31.1-b |
$1$ |
$1$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{3} \) |
$123.73809$ |
$(a^3-4a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.006865842$ |
$18873.88902$ |
2.24255 |
\( -\frac{109731163512988}{29791} a^{5} - \frac{30088797843280}{29791} a^{4} + \frac{650136482858389}{29791} a^{3} + \frac{397732842039280}{29791} a^{2} - \frac{659057925451623}{29791} a - \frac{400179289826552}{29791} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 4 a^{2} + 8 a\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 4 a + 1\) , \( a^{4} - 5 a^{2} + 3\) , \( -8 a^{5} - 4 a^{4} + 50 a^{3} + 35 a^{2} - 54 a - 31\) , \( 15 a^{5} + 6 a^{4} - 91 a^{3} - 63 a^{2} + 95 a + 60\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+4a^{2}+8a\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-4a+1\right){x}^{2}+\left(-8a^{5}-4a^{4}+50a^{3}+35a^{2}-54a-31\right){x}+15a^{5}+6a^{4}-91a^{3}-63a^{2}+95a+60$ |
31.2-a1 |
31.2-a |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$123.73809$ |
$(a^5-6a^3-a^2+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.008915534$ |
$49350.78977$ |
2.53809 |
\( -\frac{2190735616}{923521} a^{5} - \frac{905376320}{923521} a^{4} + \frac{12897504512}{923521} a^{3} + \frac{10012429312}{923521} a^{2} - \frac{11752789376}{923521} a - \frac{7484515776}{923521} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a\) , \( -4 a^{5} + 5 a^{4} + 16 a^{3} - 11 a^{2} - 11 a + 4\) , \( -3 a^{5} + 4 a^{4} + 11 a^{3} - 9 a^{2} - 6 a + 2\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(-4a^{5}+5a^{4}+16a^{3}-11a^{2}-11a+4\right){x}-3a^{5}+4a^{4}+11a^{3}-9a^{2}-6a+2$ |
31.2-a2 |
31.2-a |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$123.73809$ |
$(a^5-6a^3-a^2+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.017831069$ |
$49350.78977$ |
2.53809 |
\( \frac{24700008192}{961} a^{5} + \frac{6787114496}{961} a^{4} - \frac{146361835392}{961} a^{3} - \frac{89577473472}{961} a^{2} + \frac{148379164160}{961} a + \frac{90112462720}{961} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - 5 a^{2} + 3\) , \( 7 a^{5} - 11 a^{4} - 27 a^{3} + 31 a^{2} + 12 a - 6\) , \( 3 a^{5} - 5 a^{4} - 12 a^{3} + 14 a^{2} + 6 a - 4\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(7a^{5}-11a^{4}-27a^{3}+31a^{2}+12a-6\right){x}+3a^{5}-5a^{4}-12a^{3}+14a^{2}+6a-4$ |
31.2-b1 |
31.2-b |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$123.73809$ |
$(a^5-6a^3-a^2+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.013544559$ |
$39209.64247$ |
3.06355 |
\( -\frac{23299006720}{923521} a^{5} + \frac{14360077824}{923521} a^{4} + \frac{130747675520}{923521} a^{3} - \frac{32953242560}{923521} a^{2} - \frac{142396291584}{923521} a + \frac{40408633216}{923521} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 4 a^{2} + 7 a - 1\) , \( -a^{5} + a^{4} + 4 a^{3} - a^{2} - 2 a - 1\) , \( a^{5} - a^{4} - 4 a^{3} + a^{2} + 3 a + 2\) , \( -2 a^{5} + 2 a^{4} + 8 a^{3} - 3 a^{2} - 5 a\) , \( -a^{5} + a^{4} + 4 a^{3} - a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+4a^{2}+7a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-a^{2}-2a-1\right){x}^{2}+\left(-2a^{5}+2a^{4}+8a^{3}-3a^{2}-5a\right){x}-a^{5}+a^{4}+4a^{3}-a^{2}-3a-1$ |
31.2-b2 |
31.2-b |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$123.73809$ |
$(a^5-6a^3-a^2+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.027089119$ |
$39209.64247$ |
3.06355 |
\( -\frac{405362688}{961} a^{5} + \frac{940723136}{961} a^{4} + \frac{1332018944}{961} a^{3} - \frac{1650166272}{961} a^{2} - \frac{715969152}{961} a + \frac{289873472}{961} \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 4 a + 4\) , \( a^{3} - 4 a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 20 a^{5} + 4 a^{4} - 117 a^{3} - 66 a^{2} + 118 a + 70\) , \( 39 a^{5} + 10 a^{4} - 230 a^{3} - 139 a^{2} + 232 a + 141\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+4a+4\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(20a^{5}+4a^{4}-117a^{3}-66a^{2}+118a+70\right){x}+39a^{5}+10a^{4}-230a^{3}-139a^{2}+232a+141$ |
31.2-c1 |
31.2-c |
$1$ |
$1$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$123.73809$ |
$(a^5-6a^3-a^2+5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.013182518$ |
$33373.62523$ |
2.53786 |
\( \frac{272182}{31} a^{5} - \frac{479542}{31} a^{4} - \frac{816253}{31} a^{3} + \frac{905215}{31} a^{2} + \frac{449073}{31} a - \frac{171421}{31} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 6 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 4 a - 1\) , \( 1\) , \( 2 a^{5} - 3 a^{4} - 11 a^{3} + 11 a^{2} + 15 a - 5\) , \( -5 a^{5} + 2 a^{4} + 28 a^{3} - 2 a^{2} - 28 a + 7\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+6a\right){x}{y}+{y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+4a-1\right){x}^{2}+\left(2a^{5}-3a^{4}-11a^{3}+11a^{2}+15a-5\right){x}-5a^{5}+2a^{4}+28a^{3}-2a^{2}-28a+7$ |
41.1-a1 |
41.1-a |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$126.65488$ |
$(-a^4+2a^3+3a^2-5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.135024525$ |
$4801.442396$ |
3.73982 |
\( -\frac{53091659633408}{2825761} a^{5} - \frac{58383869558592}{2825761} a^{4} + \frac{254359500575744}{2825761} a^{3} + \frac{385906426998272}{2825761} a^{2} + \frac{52665551362176}{2825761} a - \frac{48288672078784}{2825761} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 4 a^{2} + 7 a - 1\) , \( -2 a^{5} + a^{4} + 12 a^{3} - 2 a^{2} - 14 a + 2\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 4 a + 1\) , \( -15 a^{5} + 8 a^{4} + 86 a^{3} - 19 a^{2} - 97 a + 26\) , \( -94 a^{5} + 55 a^{4} + 530 a^{3} - 126 a^{2} - 582 a + 157\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+4a^{2}+7a-1\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+4a+1\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+12a^{3}-2a^{2}-14a+2\right){x}^{2}+\left(-15a^{5}+8a^{4}+86a^{3}-19a^{2}-97a+26\right){x}-94a^{5}+55a^{4}+530a^{3}-126a^{2}-582a+157$ |
41.1-a2 |
41.1-a |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$126.65488$ |
$(-a^4+2a^3+3a^2-5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.270049050$ |
$4801.442396$ |
3.73982 |
\( -\frac{2937993472}{1681} a^{5} + \frac{55286763264}{1681} a^{4} + \frac{38369165696}{1681} a^{3} - \frac{89077707456}{1681} a^{2} - \frac{30617918720}{1681} a + \frac{14233542528}{1681} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 7 a^{2} + 4 a - 5\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 6 a + 1\) , \( a^{5} + 2 a^{4} - 4 a^{3} - 11 a^{2} - 7 a\) , \( 3 a^{5} + 5 a^{4} - 13 a^{3} - 31 a^{2} - 12 a + 4\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+6a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+7a^{2}+4a-5\right){x}^{2}+\left(a^{5}+2a^{4}-4a^{3}-11a^{2}-7a\right){x}+3a^{5}+5a^{4}-13a^{3}-31a^{2}-12a+4$ |
47.1-a1 |
47.1-a |
$2$ |
$5$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( -47 \) |
$128.10461$ |
$(2a^5-a^4-10a^3+8a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$4.667511436$ |
$0.191559365$ |
3.22356 |
\( \frac{7311665291966906351947241528318565373890469}{47} a^{5} - \frac{4346954806112764409148136193536185564093647}{47} a^{4} - 878417578200993987253098866163900427396856 a^{3} + \frac{9921932903976042368279319434408749783081233}{47} a^{2} + \frac{45282837527200374048911690129686890606008500}{47} a - \frac{12298367875041277280162183332857563285605726}{47} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 6 a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} - 1\) , \( a^{4} - 5 a^{2} - a + 4\) , \( 915 a^{5} - 493 a^{4} - 5119 a^{3} + 938 a^{2} + 5380 a - 1450\) , \( 20553 a^{5} - 11707 a^{4} - 115726 a^{3} + 25140 a^{2} + 124898 a - 33781\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+6a\right){x}{y}+\left(a^{4}-5a^{2}-a+4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}-1\right){x}^{2}+\left(915a^{5}-493a^{4}-5119a^{3}+938a^{2}+5380a-1450\right){x}+20553a^{5}-11707a^{4}-115726a^{3}+25140a^{2}+124898a-33781$ |
47.1-a2 |
47.1-a |
$2$ |
$5$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{5} \) |
$128.10461$ |
$(2a^5-a^4-10a^3+8a+1)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$0.933502287$ |
$2993.115088$ |
3.22356 |
\( \frac{13560699203902695}{229345007} a^{5} - \frac{7929093749316729}{229345007} a^{4} - \frac{1624243186618611}{4879681} a^{3} + \frac{18191504505286714}{229345007} a^{2} + \frac{83672642355273096}{229345007} a - \frac{22714159122016115}{229345007} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 6 a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} - 1\) , \( a^{4} - 5 a^{2} - a + 4\) , \( -3 a^{4} + a^{3} + 13 a^{2} - 5\) , \( 3 a^{5} - 3 a^{4} - 15 a^{3} + 10 a^{2} + 16 a - 7\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+6a\right){x}{y}+\left(a^{4}-5a^{2}-a+4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}-1\right){x}^{2}+\left(-3a^{4}+a^{3}+13a^{2}-5\right){x}+3a^{5}-3a^{4}-15a^{3}+10a^{2}+16a-7$ |
47.1-b1 |
47.1-b |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{2} \) |
$128.10461$ |
$(2a^5-a^4-10a^3+8a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.077325710$ |
$14592.51725$ |
3.25455 |
\( -\frac{122363909152}{2209} a^{5} - \frac{353980534185}{2209} a^{4} + \frac{13712106163}{47} a^{3} + \frac{1867875152277}{2209} a^{2} + \frac{371889180641}{2209} a - \frac{253512521526}{2209} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 7 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 43 a^{5} + 13 a^{4} - 250 a^{3} - 162 a^{2} + 238 a + 149\) , \( 1481 a^{5} + 402 a^{4} - 8776 a^{3} - 5351 a^{2} + 8915 a + 5407\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+7a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){x}^{2}+\left(43a^{5}+13a^{4}-250a^{3}-162a^{2}+238a+149\right){x}+1481a^{5}+402a^{4}-8776a^{3}-5351a^{2}+8915a+5407$ |
47.1-b2 |
47.1-b |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( -47 \) |
$128.10461$ |
$(2a^5-a^4-10a^3+8a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.038662855$ |
$58370.06901$ |
3.25455 |
\( -\frac{112054}{47} a^{5} + \frac{135326}{47} a^{4} + 3564 a^{3} - \frac{236727}{47} a^{2} + \frac{990128}{47} a + \frac{591223}{47} \) |
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 5 a - 2\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a + 1\) , \( 2 a^{5} - 6 a^{4} - 8 a^{3} + 21 a^{2} + 4 a - 5\) , \( 2 a^{5} + 3 a^{4} - 2 a^{3} - a^{2} - a - 1\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+5a-2\right){x}^{2}+\left(2a^{5}-6a^{4}-8a^{3}+21a^{2}+4a-5\right){x}+2a^{5}+3a^{4}-2a^{3}-a^{2}-a-1$ |
47.1-c1 |
47.1-c |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{3} \) |
$128.10461$ |
$(2a^5-a^4-10a^3+8a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.730692265$ |
$9848.125790$ |
3.45918 |
\( -\frac{17423948856}{103823} a^{5} + \frac{32224157618}{103823} a^{4} + \frac{983487568}{2209} a^{3} - \frac{58467426169}{103823} a^{2} - \frac{16161959950}{103823} a + \frac{8118919534}{103823} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 8 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( a^{5} - a^{4} - 4 a^{3} + a^{2} + 2 a + 2\) , \( 2 a^{5} - a^{4} - 3 a^{3} + 8 a^{2} - 2 a - 3\) , \( a^{5} + 5 a^{4} + 3 a^{3} - 5 a^{2} - 2 a - 4\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+8a+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}^{2}+\left(2a^{5}-a^{4}-3a^{3}+8a^{2}-2a-3\right){x}+a^{5}+5a^{4}+3a^{3}-5a^{2}-2a-4$ |
47.1-c2 |
47.1-c |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{6} \) |
$128.10461$ |
$(2a^5-a^4-10a^3+8a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.461384530$ |
$2462.031447$ |
3.45918 |
\( -\frac{13169624002415294460}{10779215329} a^{5} + \frac{11051641656481798944}{10779215329} a^{4} + \frac{1701450255542701371}{229345007} a^{3} - \frac{22980291315465018760}{10779215329} a^{2} - \frac{89116353692889766688}{10779215329} a + \frac{24473444901511420531}{10779215329} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 12 a\) , \( -a^{3} + a^{2} + 4 a\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 5 a^{2} + 10 a - 2\) , \( a^{5} - 2 a^{4} + a^{3} - 6 a^{2} + 2 a - 2\) , \( 44 a^{5} - 77 a^{4} - 134 a^{3} + 152 a^{2} + 64 a - 34\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+12a\right){x}{y}+\left(2a^{5}-2a^{4}-10a^{3}+5a^{2}+10a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(a^{5}-2a^{4}+a^{3}-6a^{2}+2a-2\right){x}+44a^{5}-77a^{4}-134a^{3}+152a^{2}+64a-34$ |
47.1-c3 |
47.1-c |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( -47 \) |
$128.10461$ |
$(2a^5-a^4-10a^3+8a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$2.192076796$ |
$13.50908887$ |
3.45918 |
\( -\frac{28879258550583535046}{47} a^{5} + \frac{50245675129623334891}{47} a^{4} + 1826835480990573116 a^{3} - \frac{91641090704900686350}{47} a^{2} - \frac{42721984192460820482}{47} a + \frac{16595437813598028248}{47} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 8 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( a^{5} - a^{4} - 4 a^{3} + a^{2} + 2 a + 2\) , \( -8 a^{5} - 31 a^{4} + 47 a^{3} + 233 a^{2} + 8 a - 303\) , \( -115 a^{5} - 321 a^{4} + 732 a^{3} + 2198 a^{2} - 452 a - 2502\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+8a+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}^{2}+\left(-8a^{5}-31a^{4}+47a^{3}+233a^{2}+8a-303\right){x}-115a^{5}-321a^{4}+732a^{3}+2198a^{2}-452a-2502$ |
47.1-c4 |
47.1-c |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{2} \) |
$128.10461$ |
$(2a^5-a^4-10a^3+8a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \) |
$4.384153592$ |
$3.377272218$ |
3.45918 |
\( -\frac{75821309689134022723951748286711}{2209} a^{5} + \frac{45077529317576597089391356811775}{2209} a^{4} + \frac{9109111067533549523397256431243}{47} a^{3} - \frac{102889549423672042160351921526305}{2209} a^{2} - \frac{469578941410894597000984454636639}{2209} a + \frac{127532965759371695390923008872004}{2209} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{2} - a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a - 1\) , \( -835 a^{5} + 1228 a^{4} + 3259 a^{3} - 3308 a^{2} - 1155 a + 468\) , \( -23404 a^{5} + 32976 a^{4} + 94727 a^{3} - 87946 a^{2} - 42025 a + 16000\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a-1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-835a^{5}+1228a^{4}+3259a^{3}-3308a^{2}-1155a+468\right){x}-23404a^{5}+32976a^{4}+94727a^{3}-87946a^{2}-42025a+16000$ |
49.1-a1 |
49.1-a |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{8} \) |
$128.55026$ |
$(a^5-a^4-4a^3+a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2301.810889$ |
1.10651 |
\( \frac{53575472896}{2401} a^{5} - \frac{283530176}{343} a^{4} - \frac{250295557376}{2401} a^{3} + \frac{25487376896}{2401} a^{2} + \frac{37330033536}{343} a - \frac{68479109056}{2401} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 7 a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 5\) , \( a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a\) , \( 6 a^{5} + 2 a^{4} - 33 a^{3} - 20 a^{2} + 21 a + 2\) , \( -5 a^{5} - 9 a^{4} + 24 a^{3} + 54 a^{2} + 12 a - 16\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+7a+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-2a-5\right){x}^{2}+\left(6a^{5}+2a^{4}-33a^{3}-20a^{2}+21a+2\right){x}-5a^{5}-9a^{4}+24a^{3}+54a^{2}+12a-16$ |
49.1-a2 |
49.1-a |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$128.55026$ |
$(a^5-a^4-4a^3+a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2301.810889$ |
1.10651 |
\( -\frac{8747175644540160}{7} a^{5} + \frac{36402793325524992}{49} a^{4} + \frac{345739071092514432}{49} a^{3} - \frac{11869921062645312}{7} a^{2} - \frac{379213000579658752}{49} a + \frac{102990475836840320}{49} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 12 a + 1\) , \( -a^{3} + 2 a\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a + 1\) , \( 10 a^{5} - 6 a^{4} - 56 a^{3} + 15 a^{2} + 62 a - 20\) , \( 33 a^{5} - 25 a^{4} - 187 a^{3} + 72 a^{2} + 218 a - 72\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+12a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a+1\right){y}={x}^{3}+\left(-a^{3}+2a\right){x}^{2}+\left(10a^{5}-6a^{4}-56a^{3}+15a^{2}+62a-20\right){x}+33a^{5}-25a^{4}-187a^{3}+72a^{2}+218a-72$ |
49.1-b1 |
49.1-b |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$128.55026$ |
$(a^5-a^4-4a^3+a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2382.794392$ |
0.572719 |
\( \frac{698570}{7} a^{5} - \frac{21719066}{343} a^{4} - \frac{193537494}{343} a^{3} + \frac{7684952}{49} a^{2} + \frac{215704780}{343} a - \frac{61744507}{343} \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 4 a + 3\) , \( a^{5} - 5 a^{3} - 3 a^{2} + 3 a + 3\) , \( 0\) , \( 3 a^{5} - 17 a^{3} - 7 a^{2} + 16 a + 9\) , \( 0\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+4a+3\right){x}{y}={x}^{3}+\left(a^{5}-5a^{3}-3a^{2}+3a+3\right){x}^{2}+\left(3a^{5}-17a^{3}-7a^{2}+16a+9\right){x}$ |
49.1-b2 |
49.1-b |
$2$ |
$2$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{12} \) |
$128.55026$ |
$(a^5-a^4-4a^3+a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1191.397196$ |
0.572719 |
\( -\frac{4793780444955809}{117649} a^{5} + \frac{407351823366500}{16807} a^{4} + \frac{27067819136018657}{117649} a^{3} - \frac{6513471065908679}{117649} a^{2} - \frac{4241329314204984}{16807} a + \frac{8072123654099021}{117649} \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 4 a + 3\) , \( a^{5} - 5 a^{3} - 3 a^{2} + 3 a + 3\) , \( 0\) , \( -12 a^{5} + 68 a^{3} + 28 a^{2} - 64 a - 36\) , \( -75 a^{5} - 16 a^{4} + 439 a^{3} + 251 a^{2} - 436 a - 261\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+4a+3\right){x}{y}={x}^{3}+\left(a^{5}-5a^{3}-3a^{2}+3a+3\right){x}^{2}+\left(-12a^{5}+68a^{3}+28a^{2}-64a-36\right){x}-75a^{5}-16a^{4}+439a^{3}+251a^{2}-436a-261$ |
49.2-a1 |
49.2-a |
$1$ |
$1$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{9} \) |
$128.55026$ |
$(-a^4+a^3+4a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.013836546$ |
$21481.38510$ |
3.42915 |
\( 45495 a^{5} - 3774 a^{4} - 244034 a^{3} - 57916 a^{2} + 180059 a - 40036 \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 13 a + 1\) , \( -a^{5} + 6 a^{3} + a^{2} - 6 a + 1\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 8 a + 3\) , \( -5 a^{5} + a^{4} + 31 a^{3} + a^{2} - 33 a + 4\) , \( -7 a^{5} + 6 a^{4} + 35 a^{3} - 10 a^{2} - 32 a + 6\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+13a+1\right){x}{y}+\left(a^{5}-6a^{3}-2a^{2}+8a+3\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-6a+1\right){x}^{2}+\left(-5a^{5}+a^{4}+31a^{3}+a^{2}-33a+4\right){x}-7a^{5}+6a^{4}+35a^{3}-10a^{2}-32a+6$ |
49.2-b1 |
49.2-b |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$128.55026$ |
$(-a^4+a^3+4a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$0.075863861$ |
$1727.109938$ |
3.40121 |
\( 7023555026985694166784 a^{5} - 9648887366434646044480 a^{4} - 28885788338374354679552 a^{3} + 25635887672503641709056 a^{2} + 13946567436683584709504 a - 5112540269534105084096 \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 4\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 4 a^{2} + 7 a\) , \( -13 a^{5} + 6 a^{4} + 47 a^{3} - 61 a^{2} - 76 a - 16\) , \( 199 a^{5} + 89 a^{4} - 681 a^{3} - 439 a^{2} + 97 a + 73\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a-1\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+4a^{2}+7a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+4\right){x}^{2}+\left(-13a^{5}+6a^{4}+47a^{3}-61a^{2}-76a-16\right){x}+199a^{5}+89a^{4}-681a^{3}-439a^{2}+97a+73$ |
49.2-b2 |
49.2-b |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$128.55026$ |
$(-a^4+a^3+4a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.025287953$ |
$46631.96834$ |
3.40121 |
\( 7229184 a^{5} - 9936448 a^{4} - 29730048 a^{3} + 26409216 a^{2} + 14360192 a - 5264576 \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 4\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 4 a^{2} + 7 a\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 11 a^{2} + 14 a + 9\) , \( a^{5} + a^{4} - 8 a^{3} - 9 a^{2} + 10 a + 7\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a-1\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+4a^{2}+7a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+4\right){x}^{2}+\left(2a^{5}+a^{4}-13a^{3}-11a^{2}+14a+9\right){x}+a^{5}+a^{4}-8a^{3}-9a^{2}+10a+7$ |
49.2-b3 |
49.2-b |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$128.55026$ |
$(-a^4+a^3+4a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.012643976$ |
$93263.93669$ |
3.40121 |
\( -677120 a^{5} + 1182464 a^{4} + 2016384 a^{3} - 2159296 a^{2} - 1004032 a + 393856 \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 7 a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + a^{2} + 2 a + 1\) , \( -a^{5} - a^{4} + 9 a^{3} + 3 a^{2} - 8 a - 1\) , \( a^{5} - 8 a^{3} + 6 a^{2} + 4 a - 2\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+7a+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-a^{5}-a^{4}+9a^{3}+3a^{2}-8a-1\right){x}+a^{5}-8a^{3}+6a^{2}+4a-2$ |
49.2-b4 |
49.2-b |
$4$ |
$6$ |
6.6.1081856.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$128.55026$ |
$(-a^4+a^3+4a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$0.037931930$ |
$3454.219877$ |
3.40121 |
\( 12308760270848 a^{5} + 28874105852416 a^{4} - 6662502842752 a^{3} - 40744939056320 a^{2} - 8372520666624 a + 5331447389056 \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 4 a^{2} + 7 a - 1\) , \( -a^{5} + 5 a^{3} + 2 a^{2} - 3 a - 1\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 8 a + 2\) , \( 254 a^{5} - 157 a^{4} - 1418 a^{3} + 347 a^{2} + 1554 a - 427\) , \( 3222 a^{5} - 1951 a^{4} - 18064 a^{3} + 4382 a^{2} + 19644 a - 5338\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+4a^{2}+7a-1\right){x}{y}+\left(a^{5}-6a^{3}-2a^{2}+8a+2\right){y}={x}^{3}+\left(-a^{5}+5a^{3}+2a^{2}-3a-1\right){x}^{2}+\left(254a^{5}-157a^{4}-1418a^{3}+347a^{2}+1554a-427\right){x}+3222a^{5}-1951a^{4}-18064a^{3}+4382a^{2}+19644a-5338$ |
*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.