| 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 |
| 2.1-a1 |
2.1-a |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$36.73340$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1471.125069$ |
1.91778527 |
\( \frac{38612253}{4} a^{4} - 17189978 a^{3} - 39860096 a^{2} + \frac{134107665}{4} a + \frac{118005317}{4} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3\) , \( -a^{4} + a^{3} + 6 a^{2} - a - 5\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 5 a^{4} - 18 a^{3} + 3 a^{2} + 50 a - 19\) , \( 7 a^{4} - 36 a^{3} + 25 a^{2} + 112 a - 55\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-a-5\right){x}^{2}+\left(5a^{4}-18a^{3}+3a^{2}+50a-19\right){x}+7a^{4}-36a^{3}+25a^{2}+112a-55$ |
| 2.1-a2 |
2.1-a |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$36.73340$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$735.5625345$ |
1.91778527 |
\( -\frac{347407763279705}{16} a^{4} + \frac{123559579559993}{2} a^{3} + \frac{138519839322317}{4} a^{2} - \frac{2205397840702053}{16} a + \frac{821982547313539}{16} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 2 a - 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a - 3\) , \( 2 a^{4} - 9 a^{3} - 3 a^{2} + 20 a - 9\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+2a-1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a\right){x}^{2}+\left(a^{4}-a^{3}-3a^{2}+4a-3\right){x}+2a^{4}-9a^{3}-3a^{2}+20a-9$ |
| 2.1-b1 |
2.1-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$36.73340$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$0.297936689$ |
$582.1544722$ |
1.13053136 |
\( -\frac{49614921476871042165389200041}{16} a^{4} + \frac{4728102009895627655218150011}{2} a^{3} + \frac{61318224529309629403565987533}{4} a^{2} + \frac{55483041245914317421631499803}{16} a - \frac{80177163286129881264229188029}{16} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{4} - 3 a^{3} + 6 a - 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -2903 a^{4} + 4432 a^{3} + 13470 a^{2} - 8078 a - 12294\) , \( 126035 a^{4} - 192204 a^{3} - 593902 a^{2} + 352690 a + 542046\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{4}-3a^{3}+6a-4\right){x}^{2}+\left(-2903a^{4}+4432a^{3}+13470a^{2}-8078a-12294\right){x}+126035a^{4}-192204a^{3}-593902a^{2}+352690a+542046$ |
| 2.1-b2 |
2.1-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$36.73340$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$0.029793668$ |
$5821.544722$ |
1.13053136 |
\( \frac{643897}{1024} a^{4} - \frac{102985}{128} a^{3} - \frac{650445}{256} a^{2} + \frac{1528149}{1024} a + \frac{1961773}{1024} \) |
\( \bigl[1\) , \( -a^{4} + a^{3} + 6 a^{2} - 7\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-7\right){x}^{2}+\left(a^{3}-2a^{2}-2a+5\right){x}+a-1$ |
| 2.1-b3 |
2.1-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{20} \) |
$36.73340$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$0.059587337$ |
$2910.772361$ |
1.13053136 |
\( -\frac{202755819017}{1048576} a^{4} + \frac{52665021849}{131072} a^{3} + \frac{143828793821}{262144} a^{2} - \frac{735606334693}{1048576} a + \frac{186325767619}{1048576} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{4} - 3 a^{3} + 6 a - 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 32 a^{4} - 48 a^{3} - 150 a^{2} + 87 a + 136\) , \( -68 a^{4} + 105 a^{3} + 323 a^{2} - 192 a - 298\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{4}-3a^{3}+6a-4\right){x}^{2}+\left(32a^{4}-48a^{3}-150a^{2}+87a+136\right){x}-68a^{4}+105a^{3}+323a^{2}-192a-298$ |
| 2.1-b4 |
2.1-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$36.73340$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$0.148968344$ |
$1164.308944$ |
1.13053136 |
\( \frac{67414803450012505}{4} a^{4} + 11415196857224997 a^{3} - 36805012364856254 a^{2} - \frac{56720491743749963}{4} a + \frac{50406441290652989}{4} \) |
\( \bigl[1\) , \( -a^{4} + a^{3} + 6 a^{2} - 7\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( -335 a^{4} + 531 a^{3} + 1558 a^{2} - 1012 a - 1475\) , \( 5948 a^{4} - 9173 a^{3} - 28039 a^{2} + 16975 a + 25811\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-7\right){x}^{2}+\left(-335a^{4}+531a^{3}+1558a^{2}-1012a-1475\right){x}+5948a^{4}-9173a^{3}-28039a^{2}+16975a+25811$ |
| 2.1-c1 |
2.1-c |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$36.73340$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2^{2} \) |
$1$ |
$0.822325043$ |
1.33999727 |
\( -\frac{49614921476871042165389200041}{16} a^{4} + \frac{4728102009895627655218150011}{2} a^{3} + \frac{61318224529309629403565987533}{4} a^{2} + \frac{55483041245914317421631499803}{16} a - \frac{80177163286129881264229188029}{16} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -a^{3} + 3 a^{2} + a - 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 1\) , \( -1400 a^{4} + 2282 a^{3} + 6169 a^{2} - 3916 a - 5657\) , \( -39459 a^{4} + 62630 a^{3} + 179590 a^{2} - 110829 a - 164083\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-5\right){x}^{2}+\left(-1400a^{4}+2282a^{3}+6169a^{2}-3916a-5657\right){x}-39459a^{4}+62630a^{3}+179590a^{2}-110829a-164083$ |
| 2.1-c2 |
2.1-c |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$36.73340$ |
$(-a)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$5139.531518$ |
1.33999727 |
\( \frac{643897}{1024} a^{4} - \frac{102985}{128} a^{3} - \frac{650445}{256} a^{2} + \frac{1528149}{1024} a + \frac{1961773}{1024} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 1\) , \( -a^{4} + 3 a^{3} + a^{2} - 5 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( -4 a^{4} + 8 a^{3} + 15 a^{2} - 18 a - 8\) , \( -a^{4} + 3 a^{3} + a^{2} - 7 a + 2\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+3a+1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+4\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+a^{2}-5a+2\right){x}^{2}+\left(-4a^{4}+8a^{3}+15a^{2}-18a-8\right){x}-a^{4}+3a^{3}+a^{2}-7a+2$ |
| 2.1-c3 |
2.1-c |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{20} \) |
$36.73340$ |
$(-a)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$2569.765759$ |
1.33999727 |
\( -\frac{202755819017}{1048576} a^{4} + \frac{52665021849}{131072} a^{3} + \frac{143828793821}{262144} a^{2} - \frac{735606334693}{1048576} a + \frac{186325767619}{1048576} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 2 a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 179 a^{4} - 274 a^{3} - 842 a^{2} + 494 a + 766\) , \( 887 a^{4} - 1362 a^{3} - 4177 a^{2} + 2487 a + 3809\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+2a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+3a+1\right){x}^{2}+\left(179a^{4}-274a^{3}-842a^{2}+494a+766\right){x}+887a^{4}-1362a^{3}-4177a^{2}+2487a+3809$ |
| 2.1-c4 |
2.1-c |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$36.73340$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$1.644650086$ |
1.33999727 |
\( \frac{67414803450012505}{4} a^{4} + 11415196857224997 a^{3} - 36805012364856254 a^{2} - \frac{56720491743749963}{4} a + \frac{50406441290652989}{4} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{4} - a^{3} - 5 a^{2} - a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 5\) , \( -149 a^{4} + 223 a^{3} + 712 a^{2} - 372 a - 730\) , \( -1682 a^{4} + 2456 a^{3} + 8186 a^{2} - 4196 a - 8085\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-a+3\right){x}^{2}+\left(-149a^{4}+223a^{3}+712a^{2}-372a-730\right){x}-1682a^{4}+2456a^{3}+8186a^{2}-4196a-8085$ |
| 2.1-d1 |
2.1-d |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$36.73340$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.013306398$ |
$17194.73767$ |
1.49133929 |
\( \frac{38612253}{4} a^{4} - 17189978 a^{3} - 39860096 a^{2} + \frac{134107665}{4} a + \frac{118005317}{4} \) |
\( \bigl[1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( a^{4} - 6 a^{3} + 2 a^{2} + 13 a - 7\) , \( -3 a^{4} + 9 a^{3} + 6 a^{2} - 21 a + 5\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+2a+1\right){x}^{2}+\left(a^{4}-6a^{3}+2a^{2}+13a-7\right){x}-3a^{4}+9a^{3}+6a^{2}-21a+5$ |
| 2.1-d2 |
2.1-d |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$36.73340$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.026612796$ |
$8597.368837$ |
1.49133929 |
\( -\frac{347407763279705}{16} a^{4} + \frac{123559579559993}{2} a^{3} + \frac{138519839322317}{4} a^{2} - \frac{2205397840702053}{16} a + \frac{821982547313539}{16} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 3 a + 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( 59 a^{4} - 167 a^{3} - 95 a^{2} + 370 a - 135\) , \( -419 a^{4} + 1192 a^{3} + 668 a^{2} - 2659 a + 991\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+3a+3\right){x}^{2}+\left(59a^{4}-167a^{3}-95a^{2}+370a-135\right){x}-419a^{4}+1192a^{3}+668a^{2}-2659a+991$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$42.19560$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1391.687916$ |
1.81422956 |
\( 6138 a^{4} - 15497 a^{3} - 12876 a^{2} + 34148 a - 7508 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{4} + a^{3} + 4 a^{2} + a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( 7 a^{4} - 24 a^{3} - 5 a^{2} + 58 a - 24\) , \( 34 a^{4} - 99 a^{3} - 51 a^{2} + 224 a - 85\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}+a-1\right){x}^{2}+\left(7a^{4}-24a^{3}-5a^{2}+58a-24\right){x}+34a^{4}-99a^{3}-51a^{2}+224a-85$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$42.19560$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$2783.375832$ |
1.81422956 |
\( -170446532 a^{4} + 491019891 a^{3} + 270844928 a^{2} - 1094370175 a + 408646686 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 2 a + 2\) , \( a^{2} - a - 2\) , \( 19 a^{4} - 56 a^{3} - 23 a^{2} + 122 a - 68\) , \( 198 a^{4} - 532 a^{3} - 372 a^{2} + 1151 a - 386\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-2a+2\right){x}^{2}+\left(19a^{4}-56a^{3}-23a^{2}+122a-68\right){x}+198a^{4}-532a^{3}-372a^{2}+1151a-386$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$42.19560$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1391.687916$ |
1.81422956 |
\( 139855256235025 a^{4} + 94995663763607 a^{3} - 304902051913729 a^{2} - 117631938280982 a + 104398850322924 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 2 a + 2\) , \( a^{2} - a - 2\) , \( -46 a^{4} + 49 a^{3} + 282 a^{2} - 88 a - 368\) , \( 682 a^{4} - 1288 a^{3} - 2653 a^{2} + 2581 a + 1758\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-2a+2\right){x}^{2}+\left(-46a^{4}+49a^{3}+282a^{2}-88a-368\right){x}+682a^{4}-1288a^{3}-2653a^{2}+2581a+1758$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$42.19560$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$347.9219790$ |
1.81422956 |
\( -196899167397644501 a^{4} + 560235687430537097 a^{3} + 314033749390697041 a^{2} - 1249946151122266014 a + 465872371548084688 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a\) , \( a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( 92 a^{4} - 71 a^{3} - 453 a^{2} - 99 a + 144\) , \( 823 a^{4} - 628 a^{3} - 4068 a^{2} - 918 a + 1328\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+2a\right){x}^{2}+\left(92a^{4}-71a^{3}-453a^{2}-99a+144\right){x}+823a^{4}-628a^{3}-4068a^{2}-918a+1328$ |
| 8.1-b1 |
8.1-b |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$42.19560$ |
$(-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.300462466$ |
$6338.239900$ |
3.10326810 |
\( 6138 a^{4} - 15497 a^{3} - 12876 a^{2} + 34148 a - 7508 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( a^{4} - a^{3} - 4 a^{2} - a + 3\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( -a^{4} - 3 a^{3} + 4 a^{2} + 5 a - 1\) , \( -7 a^{4} - 8 a^{3} + 15 a^{2} + 11 a - 6\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+a+4\right){x}{y}+\left(a^{3}-2a^{2}-2a+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}-a+3\right){x}^{2}+\left(-a^{4}-3a^{3}+4a^{2}+5a-1\right){x}-7a^{4}-8a^{3}+15a^{2}+11a-6$ |
| 8.1-b2 |
8.1-b |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$42.19560$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.600924933$ |
$3169.119950$ |
3.10326810 |
\( -170446532 a^{4} + 491019891 a^{3} + 270844928 a^{2} - 1094370175 a + 408646686 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4\) , \( -a^{2} + a + 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( 5 a^{4} - 18 a^{3} - 5 a^{2} + 44 a - 16\) , \( -16 a^{4} + 40 a^{3} + 32 a^{2} - 86 a + 24\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(5a^{4}-18a^{3}-5a^{2}+44a-16\right){x}-16a^{4}+40a^{3}+32a^{2}-86a+24$ |
| 8.1-b3 |
8.1-b |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$42.19560$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1.201849867$ |
$99.03499844$ |
3.10326810 |
\( 139855256235025 a^{4} + 94995663763607 a^{3} - 304902051913729 a^{2} - 117631938280982 a + 104398850322924 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4\) , \( -a^{2} + a + 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( -15 a^{4} - 3 a^{3} + 70 a^{2} + 14 a - 76\) , \( -131 a^{4} + 100 a^{3} + 441 a^{2} - 217 a - 286\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-15a^{4}-3a^{3}+70a^{2}+14a-76\right){x}-131a^{4}+100a^{3}+441a^{2}-217a-286$ |
| 8.1-b4 |
8.1-b |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$42.19560$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.300462466$ |
$1584.559975$ |
3.10326810 |
\( -196899167397644501 a^{4} + 560235687430537097 a^{3} + 314033749390697041 a^{2} - 1249946151122266014 a + 465872371548084688 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 4\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( -3 a^{4} + 13 a^{3} - 19 a^{2} - 11 a + 16\) , \( 8 a^{4} - 46 a^{3} + 27 a^{2} + 42 a - 16\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+4\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+5a+2\right){x}^{2}+\left(-3a^{4}+13a^{3}-19a^{2}-11a+16\right){x}+8a^{4}-46a^{3}+27a^{2}+42a-16$ |
| 10.1-a1 |
10.1-a |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{26} \cdot 5^{6} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$192.1462465$ |
1.50291195 |
\( \frac{2087460444340380311}{1048576000000} a^{4} + \frac{176786583771079417}{131072000000} a^{3} - \frac{1137816527592091459}{262144000000} a^{2} - \frac{1749279946024582853}{1048576000000} a + \frac{1557734273701059299}{1048576000000} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} - a + 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 2 a\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( -46 a^{4} + 157 a^{3} - 51 a^{2} - 120 a + 52\) , \( -52 a^{4} + 178 a^{3} - 61 a^{2} - 135 a + 60\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}-a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-2a\right){x}^{2}+\left(-46a^{4}+157a^{3}-51a^{2}-120a+52\right){x}-52a^{4}+178a^{3}-61a^{2}-135a+60$ |
| 10.1-a2 |
10.1-a |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5^{3} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$768.5849861$ |
1.50291195 |
\( -\frac{3197161119593}{1024000} a^{4} + \frac{1139988884729}{128000} a^{3} + \frac{1260088713917}{256000} a^{2} - \frac{20356474968261}{1024000} a + \frac{7695874216163}{1024000} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a + 2\) , \( a^{2} - a - 1\) , \( -a^{4} - 5 a^{3} + 8 a + 2\) , \( -11 a^{4} - 8 a^{3} + 23 a^{2} + 11 a - 8\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+4a+2\right){x}^{2}+\left(-a^{4}-5a^{3}+8a+2\right){x}-11a^{4}-8a^{3}+23a^{2}+11a-8$ |
| 10.1-b1 |
10.1-b |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{3} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$892.7944253$ |
2.32772595 |
\( \frac{4200569307133443}{250} a^{4} - \frac{7428173045756866}{125} a^{3} + \frac{3012924776455366}{125} a^{2} + \frac{11751539490804961}{250} a - \frac{5465494847310763}{250} \) |
\( \bigl[a^{2} - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 111 a^{4} - 77 a^{3} - 565 a^{2} - 127 a + 191\) , \( -1324 a^{4} + 1050 a^{3} + 6462 a^{2} + 1417 a - 2101\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+2a-2\right){x}^{2}+\left(111a^{4}-77a^{3}-565a^{2}-127a+191\right){x}-1324a^{4}+1050a^{3}+6462a^{2}+1417a-2101$ |
| 10.1-b2 |
10.1-b |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{6} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3571.177701$ |
2.32772595 |
\( \frac{60496959211}{62500} a^{4} - \frac{54202634566}{15625} a^{3} + \frac{24458292566}{15625} a^{2} + \frac{160499297447}{62500} a - \frac{76637568101}{62500} \) |
\( \bigl[a^{2} - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 6 a^{4} - 2 a^{3} - 30 a^{2} - 12 a + 11\) , \( -25 a^{4} + 20 a^{3} + 127 a^{2} + 33 a - 43\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+2a-2\right){x}^{2}+\left(6a^{4}-2a^{3}-30a^{2}-12a+11\right){x}-25a^{4}+20a^{3}+127a^{2}+33a-43$ |
| 10.1-b3 |
10.1-b |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{3} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3571.177701$ |
2.32772595 |
\( \frac{8351307}{250} a^{4} - \frac{6354384}{125} a^{3} - \frac{19931116}{125} a^{2} + \frac{23622789}{250} a + \frac{36943263}{250} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 3 a^{4} - 4 a^{3} - 9 a^{2} + 2\) , \( a^{4} - 2 a^{3} + a^{2} + 4 a - 2\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+a-2\right){x}^{2}+\left(3a^{4}-4a^{3}-9a^{2}+2\right){x}+a^{4}-2a^{3}+a^{2}+4a-2$ |
| 10.1-b4 |
10.1-b |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$446.3972126$ |
2.32772595 |
\( \frac{206396433121941319}{3906250000} a^{4} + \frac{17389549295758693}{488281250} a^{3} - \frac{112798322351851011}{976562500} a^{2} - \frac{171827154538145637}{3906250000} a + \frac{155791694906630371}{3906250000} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{2} - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -99 a^{4} + 152 a^{3} + 469 a^{2} - 278 a - 431\) , \( -817 a^{4} + 1243 a^{3} + 3855 a^{2} - 2237 a - 3479\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(-99a^{4}+152a^{3}+469a^{2}-278a-431\right){x}-817a^{4}+1243a^{3}+3855a^{2}-2237a-3479$ |
| 10.1-c1 |
10.1-c |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{3} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$0.630190832$ |
$59.10094010$ |
1.94212350 |
\( \frac{4200569307133443}{250} a^{4} - \frac{7428173045756866}{125} a^{3} + \frac{3012924776455366}{125} a^{2} + \frac{11751539490804961}{250} a - \frac{5465494847310763}{250} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + a + 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( -39 a^{4} + 134 a^{3} - 59 a^{2} - 108 a + 53\) , \( -379 a^{4} + 1317 a^{3} - 527 a^{2} - 1041 a + 483\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+a+3\right){x}^{2}+\left(-39a^{4}+134a^{3}-59a^{2}-108a+53\right){x}-379a^{4}+1317a^{3}-527a^{2}-1041a+483$ |
| 10.1-c2 |
10.1-c |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{6} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.315095416$ |
$1891.230083$ |
1.94212350 |
\( \frac{60496959211}{62500} a^{4} - \frac{54202634566}{15625} a^{3} + \frac{24458292566}{15625} a^{2} + \frac{160499297447}{62500} a - \frac{76637568101}{62500} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + a + 5\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 2 a - 1\) , \( 9 a^{4} - 21 a^{3} - 20 a^{2} + 46 a - 16\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+a+5\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+1\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){x}^{2}+\left(2a^{4}-a^{3}-9a^{2}+2a-1\right){x}+9a^{4}-21a^{3}-20a^{2}+46a-16$ |
| 10.1-c3 |
10.1-c |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{3} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.157547708$ |
$3782.460166$ |
1.94212350 |
\( \frac{8351307}{250} a^{4} - \frac{6354384}{125} a^{3} - \frac{19931116}{125} a^{2} + \frac{23622789}{250} a + \frac{36943263}{250} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a\) , \( 3 a^{3} - 6 a^{2} - 9 a + 10\) , \( -2 a^{4} + 5 a^{3} + 3 a^{2} - 7 a\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+2a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){x}^{2}+\left(3a^{3}-6a^{2}-9a+10\right){x}-2a^{4}+5a^{3}+3a^{2}-7a$ |
| 10.1-c4 |
10.1-c |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.157547708$ |
$945.6150416$ |
1.94212350 |
\( \frac{206396433121941319}{3906250000} a^{4} + \frac{17389549295758693}{488281250} a^{3} - \frac{112798322351851011}{976562500} a^{2} - \frac{171827154538145637}{3906250000} a + \frac{155791694906630371}{3906250000} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 3 a^{2} + 2 a - 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( -18 a^{4} + 28 a^{3} + 81 a^{2} - 49 a - 71\) , \( 78 a^{4} - 118 a^{3} - 373 a^{2} + 220 a + 341\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-5\right){x}^{2}+\left(-18a^{4}+28a^{3}+81a^{2}-49a-71\right){x}+78a^{4}-118a^{3}-373a^{2}+220a+341$ |
| 10.1-d1 |
10.1-d |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{26} \cdot 5^{6} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 13 \) |
$0.003782430$ |
$2408.829650$ |
4.63225010 |
\( \frac{2087460444340380311}{1048576000000} a^{4} + \frac{176786583771079417}{131072000000} a^{3} - \frac{1137816527592091459}{262144000000} a^{2} - \frac{1749279946024582853}{1048576000000} a + \frac{1557734273701059299}{1048576000000} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} - a + 2\) , \( a\) , \( -9 a^{4} + 17 a^{3} + 24 a^{2} - 3 a - 6\) , \( -33 a^{4} + 39 a^{3} + 135 a^{2} + 18 a - 40\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}-a+2\right){x}^{2}+\left(-9a^{4}+17a^{3}+24a^{2}-3a-6\right){x}-33a^{4}+39a^{3}+135a^{2}+18a-40$ |
| 10.1-d2 |
10.1-d |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5^{3} \) |
$43.14775$ |
$(-a), (a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \cdot 13 \) |
$0.007564860$ |
$4817.659301$ |
4.63225010 |
\( -\frac{3197161119593}{1024000} a^{4} + \frac{1139988884729}{128000} a^{3} + \frac{1260088713917}{256000} a^{2} - \frac{20356474968261}{1024000} a + \frac{7695874216163}{1024000} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{2} - 1\) , \( -2 a^{4} + a^{3} + 12 a^{2} - a - 8\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 5\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(-2a^{4}+a^{3}+12a^{2}-a-8\right){x}-a^{4}+a^{3}+5a^{2}-3a-5$ |
| 16.2-a1 |
16.2-a |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$39.42603362$ |
2.56982456 |
\( -\frac{49614921476871042165389200041}{16} a^{4} + \frac{4728102009895627655218150011}{2} a^{3} + \frac{61318224529309629403565987533}{4} a^{2} + \frac{55483041245914317421631499803}{16} a - \frac{80177163286129881264229188029}{16} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a\) , \( -3354 a^{4} + 4787 a^{3} + 15356 a^{2} - 8849 a - 13857\) , \( 151078 a^{4} - 218478 a^{3} - 696616 a^{2} + 402246 a + 628666\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+2a\right){x}^{2}+\left(-3354a^{4}+4787a^{3}+15356a^{2}-8849a-13857\right){x}+151078a^{4}-218478a^{3}-696616a^{2}+402246a+628666$ |
| 16.2-a2 |
16.2-a |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{22} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1971.301681$ |
2.56982456 |
\( \frac{643897}{1024} a^{4} - \frac{102985}{128} a^{3} - \frac{650445}{256} a^{2} + \frac{1528149}{1024} a + \frac{1961773}{1024} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( 0\) , \( -2 a^{4} + 4 a^{3} + 7 a^{2} - 8 a - 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(-2a^{4}+4a^{3}+7a^{2}-8a-3\right){x}$ |
| 16.2-a3 |
16.2-a |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{32} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$985.6508406$ |
2.56982456 |
\( -\frac{202755819017}{1048576} a^{4} + \frac{52665021849}{131072} a^{3} + \frac{143828793821}{262144} a^{2} - \frac{735606334693}{1048576} a + \frac{186325767619}{1048576} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( -10 a^{4} + 41 a^{3} - 21 a^{2} - 42 a + 24\) , \( -37 a^{4} + 137 a^{3} - 56 a^{2} - 114 a + 51\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-6a-1\right){x}^{2}+\left(-10a^{4}+41a^{3}-21a^{2}-42a+24\right){x}-37a^{4}+137a^{3}-56a^{2}-114a+51$ |
| 16.2-a4 |
16.2-a |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$78.85206725$ |
2.56982456 |
\( \frac{67414803450012505}{4} a^{4} + 11415196857224997 a^{3} - 36805012364856254 a^{2} - \frac{56720491743749963}{4} a + \frac{50406441290652989}{4} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( 0\) , \( -372 a^{4} + 569 a^{3} + 1747 a^{2} - 1093 a - 1673\) , \( 6663 a^{4} - 10082 a^{3} - 31276 a^{2} + 18198 a + 28116\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(-372a^{4}+569a^{3}+1747a^{2}-1093a-1673\right){x}+6663a^{4}-10082a^{3}-31276a^{2}+18198a+28116$ |
| 16.2-b1 |
16.2-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$31.88092791$ |
2.07802774 |
\( -\frac{49614921476871042165389200041}{16} a^{4} + \frac{4728102009895627655218150011}{2} a^{3} + \frac{61318224529309629403565987533}{4} a^{2} + \frac{55483041245914317421631499803}{16} a - \frac{80177163286129881264229188029}{16} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( -1447 a^{4} + 2134 a^{3} + 6919 a^{2} - 3800 a - 6557\) , \( -48380 a^{4} + 74581 a^{3} + 226206 a^{2} - 137355 a - 204333\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+2a-1\right){x}^{2}+\left(-1447a^{4}+2134a^{3}+6919a^{2}-3800a-6557\right){x}-48380a^{4}+74581a^{3}+226206a^{2}-137355a-204333$ |
| 16.2-b2 |
16.2-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{22} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1594.046395$ |
2.07802774 |
\( \frac{643897}{1024} a^{4} - \frac{102985}{128} a^{3} - \frac{650445}{256} a^{2} + \frac{1528149}{1024} a + \frac{1961773}{1024} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + 3 a^{2} + a - 6\) , \( a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( a^{4} - 4 a^{3} - 5 a^{2} + 6 a + 5\) , \( -6 a^{4} - 2 a^{3} + 16 a^{2} + a - 9\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+4\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-6\right){x}^{2}+\left(a^{4}-4a^{3}-5a^{2}+6a+5\right){x}-6a^{4}-2a^{3}+16a^{2}+a-9$ |
| 16.2-b3 |
16.2-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{32} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$797.0231977$ |
2.07802774 |
\( -\frac{202755819017}{1048576} a^{4} + \frac{52665021849}{131072} a^{3} + \frac{143828793821}{262144} a^{2} - \frac{735606334693}{1048576} a + \frac{186325767619}{1048576} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 62 a^{4} - 47 a^{3} - 311 a^{2} - 61 a + 111\) , \( -420 a^{4} + 324 a^{3} + 2065 a^{2} + 470 a - 669\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){x}^{2}+\left(62a^{4}-47a^{3}-311a^{2}-61a+111\right){x}-420a^{4}+324a^{3}+2065a^{2}+470a-669$ |
| 16.2-b4 |
16.2-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$63.76185582$ |
2.07802774 |
\( \frac{67414803450012505}{4} a^{4} + 11415196857224997 a^{3} - 36805012364856254 a^{2} - \frac{56720491743749963}{4} a + \frac{50406441290652989}{4} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 4\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 4\) , \( a\) , \( 77 a^{4} - 450 a^{3} + 429 a^{2} + 1110 a - 1387\) , \( -8862 a^{4} + 22771 a^{3} + 19927 a^{2} - 49652 a + 8625\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+4\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-4\right){x}^{2}+\left(77a^{4}-450a^{3}+429a^{2}+1110a-1387\right){x}-8862a^{4}+22771a^{3}+19927a^{2}-49652a+8625$ |
| 16.2-c1 |
16.2-c |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1317.172196$ |
1.71708952 |
\( \frac{38612253}{4} a^{4} - 17189978 a^{3} - 39860096 a^{2} + \frac{134107665}{4} a + \frac{118005317}{4} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4\) , \( a^{3} - 3 a^{2} - a + 5\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 4\) , \( -7 a^{4} + 10 a^{3} + 34 a^{2} - 16 a - 33\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4\right){x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+5\right){x}^{2}+\left(-a^{4}+a^{3}+5a^{2}-4\right){x}-7a^{4}+10a^{3}+34a^{2}-16a-33$ |
| 16.2-c2 |
16.2-c |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$658.5860982$ |
1.71708952 |
\( -\frac{347407763279705}{16} a^{4} + \frac{123559579559993}{2} a^{3} + \frac{138519839322317}{4} a^{2} - \frac{2205397840702053}{16} a + \frac{821982547313539}{16} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 19 a^{4} - 47 a^{3} - 30 a^{2} + 107 a - 40\) , \( -44 a^{4} + 128 a^{3} + 72 a^{2} - 284 a + 103\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(19a^{4}-47a^{3}-30a^{2}+107a-40\right){x}-44a^{4}+128a^{3}+72a^{2}-284a+103$ |
| 16.2-d1 |
16.2-d |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.034764318$ |
$12067.76533$ |
2.73451915 |
\( 6138 a^{4} - 15497 a^{3} - 12876 a^{2} + 34148 a - 7508 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2\) , \( -a^{3} + 3 a^{2} + 3 a - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( -a^{4} + a^{3} + 4 a^{2} - a\) , \( -4 a^{3} + 7 a^{2} + 3 a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-4\right){x}^{2}+\left(-a^{4}+a^{3}+4a^{2}-a\right){x}-4a^{3}+7a^{2}+3a-3$ |
| 16.2-d2 |
16.2-d |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.069528637$ |
$24135.53067$ |
2.73451915 |
\( -170446532 a^{4} + 491019891 a^{3} + 270844928 a^{2} - 1094370175 a + 408646686 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 8 a^{4} - 7 a^{3} - 38 a^{2} - 4 a + 13\) , \( -17 a^{4} + 13 a^{3} + 85 a^{2} + 20 a - 28\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-3\right){x}^{2}+\left(8a^{4}-7a^{3}-38a^{2}-4a+13\right){x}-17a^{4}+13a^{3}+85a^{2}+20a-28$ |
| 16.2-d3 |
16.2-d |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{10} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.034764318$ |
$6033.882669$ |
2.73451915 |
\( 139855256235025 a^{4} + 94995663763607 a^{3} - 304902051913729 a^{2} - 117631938280982 a + 104398850322924 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 18 a^{4} - 12 a^{3} - 93 a^{2} - 29 a + 23\) , \( 80 a^{4} - 69 a^{3} - 390 a^{2} - 56 a + 148\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-3\right){x}^{2}+\left(18a^{4}-12a^{3}-93a^{2}-29a+23\right){x}+80a^{4}-69a^{3}-390a^{2}-56a+148$ |
| 16.2-d4 |
16.2-d |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{4} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.139057275$ |
$6033.882669$ |
2.73451915 |
\( -196899167397644501 a^{4} + 560235687430537097 a^{3} + 314033749390697041 a^{2} - 1249946151122266014 a + 465872371548084688 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} - a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( a^{4} - 14 a^{2} - 9 a + 14\) , \( 4 a^{3} + 12 a^{2} + 24 a + 22\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+4\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-a+3\right){x}^{2}+\left(a^{4}-14a^{2}-9a+14\right){x}+4a^{3}+12a^{2}+24a+22$ |
| 16.2-e1 |
16.2-e |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$858.3899466$ |
1.11901267 |
\( \frac{38612253}{4} a^{4} - 17189978 a^{3} - 39860096 a^{2} + \frac{134107665}{4} a + \frac{118005317}{4} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} - a + 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -10 a^{4} + 13 a^{3} + 45 a^{2} - 15 a - 29\) , \( 7 a^{4} - 15 a^{3} - 31 a^{2} + 39 a + 38\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}-a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-10a^{4}+13a^{3}+45a^{2}-15a-29\right){x}+7a^{4}-15a^{3}-31a^{2}+39a+38$ |
| 16.2-e2 |
16.2-e |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$429.1949733$ |
1.11901267 |
\( -\frac{347407763279705}{16} a^{4} + \frac{123559579559993}{2} a^{3} + \frac{138519839322317}{4} a^{2} - \frac{2205397840702053}{16} a + \frac{821982547313539}{16} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 843 a^{4} - 2398 a^{3} - 1343 a^{2} + 5345 a - 1993\) , \( 23570 a^{4} - 67063 a^{3} - 37590 a^{2} + 149620 a - 55765\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+2a\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+3a\right){x}^{2}+\left(843a^{4}-2398a^{3}-1343a^{2}+5345a-1993\right){x}+23570a^{4}-67063a^{3}-37590a^{2}+149620a-55765$ |
| 16.2-f1 |
16.2-f |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.749829510$ |
$2128.194857$ |
2.60036501 |
\( 6138 a^{4} - 15497 a^{3} - 12876 a^{2} + 34148 a - 7508 \) |
\( \bigl[a\) , \( a^{4} - a^{3} - 5 a^{2} + 3\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( -2 a^{3} + 3 a^{2} + 7 a - 3\) , \( 3 a^{4} - 7 a^{3} - 7 a^{2} + 13 a - 5\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3\right){x}^{2}+\left(-2a^{3}+3a^{2}+7a-3\right){x}+3a^{4}-7a^{3}-7a^{2}+13a-5$ |
| 16.2-f2 |
16.2-f |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.499659021$ |
$1064.097428$ |
2.60036501 |
\( -170446532 a^{4} + 491019891 a^{3} + 270844928 a^{2} - 1094370175 a + 408646686 \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( -a^{4} + 3 a^{3} + a^{2} - 7 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 4\) , \( 34 a^{4} - 92 a^{3} - 59 a^{2} + 202 a - 75\) , \( 319 a^{4} - 903 a^{3} - 513 a^{2} + 2011 a - 750\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+3a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+a^{2}-7a+3\right){x}^{2}+\left(34a^{4}-92a^{3}-59a^{2}+202a-75\right){x}+319a^{4}-903a^{3}-513a^{2}+2011a-750$ |
*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.
