| 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 |
$2$ |
$7$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{7} \) |
$37.51355$ |
$(-a)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$5798.166249$ |
2.11468640 |
\( -\frac{9723067}{4} a^{4} + \frac{530515}{4} a^{3} + \frac{19071567}{2} a^{2} - \frac{2920619}{2} a - \frac{5196193}{2} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 11 a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 3\) , \( 69 a^{4} - 168 a^{3} - 200 a^{2} + 636 a - 287\) , \( -1061 a^{4} + 2613 a^{3} + 3034 a^{2} - 9891 a + 4581\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+7a+3\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+11a+1\right){x}^{2}+\left(69a^{4}-168a^{3}-200a^{2}+636a-287\right){x}-1061a^{4}+2613a^{3}+3034a^{2}-9891a+4581$ |
| 2.1-a2 |
2.1-a |
$2$ |
$7$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$37.51355$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.344985199$ |
2.11468640 |
\( -\frac{1371586593220060076753480698677288175}{2} a^{4} + 2720652387142556710549725040138976915 a^{3} - 2608787952274119891781102438055979732 a^{2} - 354440582305826288429095048498479098 a + 697241673154855672058406960918368475 \) |
\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( 396 a^{4} + 13 a^{3} - 1490 a^{2} + 262 a + 364\) , \( -7858 a^{4} - 3450 a^{3} + 24113 a^{2} - 2085 a - 6332\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+7a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){x}^{2}+\left(396a^{4}+13a^{3}-1490a^{2}+262a+364\right){x}-7858a^{4}-3450a^{3}+24113a^{2}-2085a-6332$ |
| 2.1-b1 |
2.1-b |
$2$ |
$3$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{9} \) |
$37.51355$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1.212181300$ |
$10.53885119$ |
1.46766425 |
\( -\frac{170457143790539}{4} a^{4} + \frac{86865724365143}{4} a^{3} + \frac{810871574784419}{4} a^{2} - \frac{155193950654227}{4} a - 57333096978135 \) |
\( \bigl[a^{4} - 6 a^{2} + 5\) , \( a^{4} - 6 a^{2} + 6\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 2 a + 5\) , \( 7 a^{4} - 33 a^{3} + 16 a^{2} + 129 a - 167\) , \( 109 a^{4} - 397 a^{3} - 67 a^{2} + 1535 a - 1378\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}+5\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+2a+5\right){y}={x}^{3}+\left(a^{4}-6a^{2}+6\right){x}^{2}+\left(7a^{4}-33a^{3}+16a^{2}+129a-167\right){x}+109a^{4}-397a^{3}-67a^{2}+1535a-1378$ |
| 2.1-b2 |
2.1-b |
$2$ |
$3$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{3} \) |
$37.51355$ |
$(-a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.404060433$ |
$2560.940839$ |
1.46766425 |
\( -32868 a^{4} + \frac{6933}{2} a^{3} + \frac{260831}{2} a^{2} - 27529 a - 38860 \) |
\( \bigl[a^{4} - 6 a^{2} + 5\) , \( a^{4} - 6 a^{2} + 6\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 2 a + 5\) , \( 2 a^{4} + 2 a^{3} - 14 a^{2} - 11 a + 18\) , \( 2 a^{4} + 2 a^{3} - 13 a^{2} - 11 a + 14\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}+5\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+2a+5\right){y}={x}^{3}+\left(a^{4}-6a^{2}+6\right){x}^{2}+\left(2a^{4}+2a^{3}-14a^{2}-11a+18\right){x}+2a^{4}+2a^{3}-13a^{2}-11a+14$ |
| 2.1-c1 |
2.1-c |
$2$ |
$3$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$37.51355$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 3 \) |
$1$ |
$2.820130977$ |
1.74956025 |
\( -\frac{2659470836337409}{2} a^{4} - 400326741104443 a^{3} + \frac{8825296807669011}{2} a^{2} - 486598119825810 a - 1167918770212002 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 4\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 6 a + 4\) , \( 12 a^{4} - 34 a^{3} + 24 a + 1\) , \( 12 a^{4} - 57 a^{3} + 45 a^{2} + 16 a - 13\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+6a+4\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+7a+4\right){x}^{2}+\left(12a^{4}-34a^{3}+24a+1\right){x}+12a^{4}-57a^{3}+45a^{2}+16a-13$ |
| 2.1-c2 |
2.1-c |
$2$ |
$3$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{9} \) |
$37.51355$ |
$(-a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$685.2918276$ |
1.74956025 |
\( -\frac{29645}{2} a^{4} - \frac{44327}{4} a^{3} + \frac{95415}{2} a^{2} + \frac{81883}{4} a - 26385 \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3 a + 5\) , \( 0\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( -2 a^{4} - 2 a^{3} + 8 a^{2} + 12 a + 6\) , \( 4 a^{4} - 10 a^{3} - 20 a^{2} + 40 a + 20\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+3a+5\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a\right){y}={x}^{3}+\left(-2a^{4}-2a^{3}+8a^{2}+12a+6\right){x}+4a^{4}-10a^{3}-20a^{2}+40a+20$ |
| 4.1-a1 |
4.1-a |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$40.20603$ |
$(-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$10505.34483$ |
1.67626887 |
\( 4096 a^{4} - 16352 a^{3} + 19456 a^{2} - 6272 a + 768 \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 2 a + 6\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a\) , \( a^{4} - 5 a^{2} + 2\) , \( -8 a^{4} + 7 a^{3} + 34 a^{2} - 18 a - 3\) , \( -12 a^{4} + 7 a^{3} + 57 a^{2} - 19 a - 11\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+2a+6\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a\right){x}^{2}+\left(-8a^{4}+7a^{3}+34a^{2}-18a-3\right){x}-12a^{4}+7a^{3}+57a^{2}-19a-11$ |
| 4.1-a2 |
4.1-a |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$40.20603$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$10505.34483$ |
1.67626887 |
\( 1536 a^{3} + 64 a^{2} - 4224 a + 4864 \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 2 a + 6\) , \( -a^{4} + 6 a^{2} + a - 5\) , \( a^{4} - 5 a^{2} - a + 2\) , \( -15 a^{4} + 10 a^{3} + 65 a^{2} - 12 a - 19\) , \( -31 a^{4} + 17 a^{3} + 144 a^{2} - 27 a - 41\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+2a+6\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-5\right){x}^{2}+\left(-15a^{4}+10a^{3}+65a^{2}-12a-19\right){x}-31a^{4}+17a^{3}+144a^{2}-27a-41$ |
| 4.1-a3 |
4.1-a |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$40.20603$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$656.5840522$ |
1.67626887 |
\( 9449488 a^{4} + 4349920 a^{3} - 28573760 a^{2} + 2621576 a + 7340768 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{4} + 6 a^{2} + 2 a - 6\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( -12 a^{4} + 13 a^{3} + 60 a^{2} - 46 a - 32\) , \( -18 a^{4} + 23 a^{3} + 87 a^{2} - 80 a - 54\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+2a-6\right){x}^{2}+\left(-12a^{4}+13a^{3}+60a^{2}-46a-32\right){x}-18a^{4}+23a^{3}+87a^{2}-80a-54$ |
| 4.1-a4 |
4.1-a |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$40.20603$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2626.336208$ |
1.67626887 |
\( -3158032 a^{4} + 8568832 a^{3} + 7602240 a^{2} - 32702472 a + 19071728 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( a^{3} - 3 a\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( 14 a^{4} - 4 a^{3} - 65 a^{2} + 2 a + 14\) , \( -55 a^{4} + 29 a^{3} + 262 a^{2} - 54 a - 76\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(14a^{4}-4a^{3}-65a^{2}+2a+14\right){x}-55a^{4}+29a^{3}+262a^{2}-54a-76$ |
| 7.1-a1 |
7.1-a |
$4$ |
$6$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3502.611551$ |
1.49036991 |
\( -\frac{8004305085704}{117649} a^{4} + \frac{4141088345280}{117649} a^{3} + \frac{37991329701812}{117649} a^{2} - \frac{7545938455168}{117649} a - \frac{10474018356248}{117649} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3 a + 6\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a\) , \( a^{4} - 5 a^{2} - a + 3\) , \( -69 a^{4} - 16 a^{3} + 234 a^{2} - 38 a - 68\) , \( -893 a^{4} - 155 a^{3} + 3067 a^{2} - 637 a - 929\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+3a+6\right){x}{y}+\left(a^{4}-5a^{2}-a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a\right){x}^{2}+\left(-69a^{4}-16a^{3}+234a^{2}-38a-68\right){x}-893a^{4}-155a^{3}+3067a^{2}-637a-929$ |
| 7.1-a2 |
7.1-a |
$4$ |
$6$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$7005.223102$ |
1.49036991 |
\( \frac{23378672}{343} a^{4} - \frac{31351424}{343} a^{3} - \frac{111705344}{343} a^{2} + \frac{108384896}{343} a + \frac{69562944}{343} \) |
\( \bigl[a^{4} - 5 a^{2} + 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 6 a + 3\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 12 a - 5\) , \( -4 a^{4} + 8 a^{3} + 14 a^{2} - 29 a + 9\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+6a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(a^{4}-3a^{3}-2a^{2}+12a-5\right){x}-4a^{4}+8a^{3}+14a^{2}-29a+9$ |
| 7.1-a3 |
7.1-a |
$4$ |
$6$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{18} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$14.41403930$ |
1.49036991 |
\( \frac{1036356742091595243134623016}{1628413597910449} a^{4} + \frac{307894159614977653049053592}{1628413597910449} a^{3} - \frac{3438309916361349905128920316}{1628413597910449} a^{2} + \frac{392601561869586626501661680}{1628413597910449} a + \frac{902234770568593789020484184}{1628413597910449} \) |
\( \bigl[a\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 6 a + 3\) , \( a + 1\) , \( 746 a^{4} - 380 a^{3} - 3551 a^{2} + 672 a + 999\) , \( -3457 a^{4} + 1750 a^{3} + 16432 a^{2} - 3101 a - 4628\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+6a+3\right){x}^{2}+\left(746a^{4}-380a^{3}-3551a^{2}+672a+999\right){x}-3457a^{4}+1750a^{3}+16432a^{2}-3101a-4628$ |
| 7.1-a4 |
7.1-a |
$4$ |
$6$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{9} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3^{2} \) |
$1$ |
$28.82807861$ |
1.49036991 |
\( \frac{171167680868232798611184}{40353607} a^{4} - \frac{232790313158535191415296}{40353607} a^{3} - \frac{833653440524601099905664}{40353607} a^{2} + \frac{835814287028797507428608}{40353607} a + \frac{534910073097769495251648}{40353607} \) |
\( \bigl[a^{4} - 5 a^{2} + 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 6 a + 3\) , \( -34 a^{4} + 57 a^{3} + 143 a^{2} - 208 a - 25\) , \( -22 a^{4} - 21 a^{3} + 193 a^{2} + 99 a - 394\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+6a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(-34a^{4}+57a^{3}+143a^{2}-208a-25\right){x}-22a^{4}-21a^{3}+193a^{2}+99a-394$ |
| 7.1-b1 |
7.1-b |
$2$ |
$2$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2532.816998$ |
1.61657988 |
\( \frac{227613873195}{7} a^{4} - \frac{309558227978}{7} a^{3} - \frac{1108567285219}{7} a^{2} + \frac{1111441287226}{7} a + \frac{711307533303}{7} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 8 a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a\) , \( -8 a^{4} + 14 a^{3} + 35 a^{2} - 51 a - 10\) , \( 11 a^{4} - 17 a^{3} - 49 a^{2} + 62 a + 17\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+8a-3\right){x}^{2}+\left(-8a^{4}+14a^{3}+35a^{2}-51a-10\right){x}+11a^{4}-17a^{3}-49a^{2}+62a+17$ |
| 7.1-b2 |
7.1-b |
$2$ |
$2$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1266.408499$ |
1.61657988 |
\( \frac{210680457908622372175676}{49} a^{4} - \frac{286528213277696004126318}{49} a^{3} - \frac{1026096092985375056337269}{49} a^{2} + \frac{1028755754689926985092013}{49} a + \frac{658390056841997280187283}{49} \) |
\( \bigl[1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 8 a + 2\) , \( a + 1\) , \( 2 a^{4} - 6 a^{3} - 5 a^{2} + 29 a - 23\) , \( 19 a^{4} - 41 a^{3} - 71 a^{2} + 178 a - 67\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-8a+2\right){x}^{2}+\left(2a^{4}-6a^{3}-5a^{2}+29a-23\right){x}+19a^{4}-41a^{3}-71a^{2}+178a-67$ |
| 7.1-c1 |
7.1-c |
$2$ |
$2$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5417.270122$ |
3.45759283 |
\( \frac{72304}{7} a^{4} - \frac{168640}{7} a^{3} - \frac{221376}{7} a^{2} + \frac{621056}{7} a - \frac{231744}{7} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a\) , \( a^{4} - 5 a^{2} - a + 3\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 9 a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 5 a + 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}{y}+\left(a^{4}-5a^{2}-a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a\right){x}^{2}+\left(a^{4}-2a^{3}-5a^{2}+9a+1\right){x}+2a^{4}-2a^{3}-9a^{2}+5a+3$ |
| 7.1-c2 |
7.1-c |
$2$ |
$2$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2708.635061$ |
3.45759283 |
\( -\frac{34002502808}{49} a^{4} + \frac{83763685288}{49} a^{3} + \frac{97220367140}{49} a^{2} - \frac{317080393464}{49} a + \frac{146854872376}{49} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( -a^{3} + 2 a^{2} + 3 a - 5\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( -a^{3} - 5 a^{2} - 7 a + 6\) , \( -2 a^{4} - 6 a^{3} - a^{2} + a - 5\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-5\right){x}^{2}+\left(-a^{3}-5a^{2}-7a+6\right){x}-2a^{4}-6a^{3}-a^{2}+a-5$ |
| 7.1-d1 |
7.1-d |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1444.500816$ |
0.921958027 |
\( \frac{4933507695772136}{7} a^{4} - \frac{19572019092169272}{7} a^{3} + \frac{18767280936023972}{7} a^{2} + \frac{2549799363201464}{7} a - \frac{5015865810085112}{7} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 4\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 11 a\) , \( a^{4} - 6 a^{2} + 5\) , \( a^{4} + 6 a^{3} - 10 a^{2} - 25 a + 7\) , \( 11 a^{4} - 2 a^{3} - 57 a^{2} + 18\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+7a+4\right){x}{y}+\left(a^{4}-6a^{2}+5\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+8a^{2}-11a\right){x}^{2}+\left(a^{4}+6a^{3}-10a^{2}-25a+7\right){x}+11a^{4}-2a^{3}-57a^{2}+18$ |
| 7.1-d2 |
7.1-d |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1444.500816$ |
0.921958027 |
\( -\frac{1215331584}{7} a^{4} + \frac{615849984}{7} a^{3} + \frac{5780860160}{7} a^{2} - \frac{1090171008}{7} a - \frac{1627596800}{7} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( -a^{4} + 6 a^{2} + a - 6\) , \( 1\) , \( 5 a^{4} - 2 a^{3} - 25 a^{2} + 2 a + 11\) , \( -7 a^{4} + 2 a^{3} + 31 a^{2} - 5 a - 10\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+6a^{2}+a-6\right){x}^{2}+\left(5a^{4}-2a^{3}-25a^{2}+2a+11\right){x}-7a^{4}+2a^{3}+31a^{2}-5a-10$ |
| 7.1-d3 |
7.1-d |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2889.001633$ |
0.921958027 |
\( \frac{172575504}{49} a^{4} - \frac{679954368}{49} a^{3} + \frac{643667392}{49} a^{2} + \frac{94839296}{49} a - \frac{169464000}{49} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 8 a - 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( -7 a^{4} + 22 a^{3} - a^{2} - 27 a + 4\) , \( -29 a^{4} + 95 a^{3} - 43 a^{2} - 45 a - 10\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+8a-3\right){x}^{2}+\left(-7a^{4}+22a^{3}-a^{2}-27a+4\right){x}-29a^{4}+95a^{3}-43a^{2}-45a-10$ |
| 7.1-d4 |
7.1-d |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$361.1252041$ |
0.921958027 |
\( \frac{11672204400680}{2401} a^{4} - \frac{9069493672184}{2401} a^{3} - \frac{50472064618428}{2401} a^{2} + \frac{38499225589240}{2401} a + \frac{27218426897176}{2401} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 4\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 11 a\) , \( a^{3} - a^{2} - 3 a + 3\) , \( -19 a^{4} + 25 a^{3} + 87 a^{2} - 91 a - 41\) , \( -66 a^{4} + 79 a^{3} + 316 a^{2} - 276 a - 178\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+7a+4\right){x}{y}+\left(a^{3}-a^{2}-3a+3\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+8a^{2}-11a\right){x}^{2}+\left(-19a^{4}+25a^{3}+87a^{2}-91a-41\right){x}-66a^{4}+79a^{3}+316a^{2}-276a-178$ |
| 7.1-e1 |
7.1-e |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$4428.868794$ |
2.82674201 |
\( -\frac{709191712632}{7} a^{4} + \frac{359496015632}{7} a^{3} + \frac{3373647298116}{7} a^{2} - \frac{636157247048}{7} a - \frac{949917575480}{7} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 10 a + 1\) , \( 1\) , \( -6 a^{4} + 5 a^{3} + 27 a^{2} - 17 a - 8\) , \( a^{2} + 2 a - 1\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+10a+1\right){x}^{2}+\left(-6a^{4}+5a^{3}+27a^{2}-17a-8\right){x}+a^{2}+2a-1$ |
| 7.1-e2 |
7.1-e |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1107.217198$ |
2.82674201 |
\( \frac{271791985608}{2401} a^{4} - \frac{953008470640}{2401} a^{3} + \frac{617237947876}{2401} a^{2} + \frac{350193604088}{2401} a - \frac{77381956392}{2401} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( 2 a^{4} - a^{3} - 10 a^{2} + a + 4\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 2 a + 5\) , \( -26 a^{4} + 53 a^{3} + 85 a^{2} - 194 a + 81\) , \( 88 a^{4} - 196 a^{3} - 272 a^{2} + 731 a - 319\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+2a+5\right){y}={x}^{3}+\left(2a^{4}-a^{3}-10a^{2}+a+4\right){x}^{2}+\left(-26a^{4}+53a^{3}+85a^{2}-194a+81\right){x}+88a^{4}-196a^{3}-272a^{2}+731a-319$ |
| 7.1-e3 |
7.1-e |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$8857.737589$ |
2.82674201 |
\( -\frac{7015920}{49} a^{4} + \frac{3321408}{49} a^{3} + \frac{33961664}{49} a^{2} - \frac{6015104}{49} a - \frac{9274688}{49} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{4} + 6 a^{2} - 6\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( 2 a^{4} - 3 a^{3} - 9 a^{2} + 10 a + 3\) , \( 2 a^{4} - 9 a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-6\right){x}^{2}+\left(2a^{4}-3a^{3}-9a^{2}+10a+3\right){x}+2a^{4}-9a^{2}-2a+1$ |
| 7.1-e4 |
7.1-e |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$4428.868794$ |
2.82674201 |
\( -\frac{3365120}{7} a^{4} + \frac{8283648}{7} a^{3} + \frac{9626368}{7} a^{2} - \frac{31355008}{7} a + \frac{14518272}{7} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 10 a\) , \( a^{4} - 6 a^{2} + 5\) , \( 2 a^{3} - 2 a^{2} - 8 a + 7\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 5 a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}{y}+\left(a^{4}-6a^{2}+5\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+10a\right){x}^{2}+\left(2a^{3}-2a^{2}-8a+7\right){x}+a^{4}-2a^{3}-2a^{2}+5a-3$ |
| 7.1-f1 |
7.1-f |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1121.102679$ |
0.715547961 |
\( -\frac{1257911155088384}{7} a^{4} + \frac{637381302891008}{7} a^{3} + \frac{5983447274883840}{7} a^{2} - \frac{1128196582831232}{7} a - \frac{1684738001305088}{7} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( -a^{4} + 6 a^{2} + a - 4\) , \( a^{4} - 5 a^{2} + 3\) , \( -3 a^{4} + a^{3} + 12 a^{2} - 5 a - 2\) , \( 3 a^{4} - a^{3} - 13 a^{2} + 3 a + 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-4\right){x}^{2}+\left(-3a^{4}+a^{3}+12a^{2}-5a-2\right){x}+3a^{4}-a^{3}-13a^{2}+3a+3$ |
| 7.1-f2 |
7.1-f |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2242.205358$ |
0.715547961 |
\( \frac{3564846480}{49} a^{4} - \frac{4867513984}{49} a^{3} - \frac{17630117504}{49} a^{2} + \frac{17749822592}{49} a + \frac{12705801152}{49} \) |
\( \bigl[a^{4} - 5 a^{2} + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 1\) , \( a^{4} - 5 a^{2} + 3\) , \( 429 a^{4} - 218 a^{3} - 2042 a^{2} + 387 a + 577\) , \( 7854 a^{4} - 3980 a^{3} - 37359 a^{2} + 7045 a + 10518\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-1\right){x}^{2}+\left(429a^{4}-218a^{3}-2042a^{2}+387a+577\right){x}+7854a^{4}-3980a^{3}-37359a^{2}+7045a+10518$ |
| 7.1-f3 |
7.1-f |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1121.102679$ |
0.715547961 |
\( -\frac{501581915088248}{7} a^{4} + \frac{1490747283491280}{7} a^{3} + \frac{1391729568252948}{7} a^{2} - \frac{5504184514775200}{7} a + \frac{2645954670979048}{7} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 11 a\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 2 a + 5\) , \( -3 a^{4} + 7 a^{3} - 4 a^{2} - 6 a + 4\) , \( 10 a^{4} - 17 a^{3} - 9 a^{2} + 8 a\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+2a+5\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+11a\right){x}^{2}+\left(-3a^{4}+7a^{3}-4a^{2}-6a+4\right){x}+10a^{4}-17a^{3}-9a^{2}+8a$ |
| 7.1-f4 |
7.1-f |
$4$ |
$4$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$42.52017$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$280.2756698$ |
0.715547961 |
\( \frac{64269794737455610568}{2401} a^{4} - \frac{87407772194637887920}{2401} a^{3} - \frac{313018995095763863500}{2401} a^{2} + \frac{313830346758049426912}{2401} a + \frac{200847265112419906808}{2401} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 6 a - 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( 2 a^{4} - 18 a^{3} - a^{2} + 98 a - 58\) , \( 70 a^{4} - 141 a^{3} - 258 a^{2} + 597 a - 250\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{3}-a^{2}-4a+3\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-6a-2\right){x}^{2}+\left(2a^{4}-18a^{3}-a^{2}+98a-58\right){x}+70a^{4}-141a^{3}-258a^{2}+597a-250$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$43.09176$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$367.0008711$ |
0.936958692 |
\( -17447948598269 a^{4} - 5182193258523 a^{3} + 57888251195749 a^{2} - 6613769751515 a - 15191886995724 \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3 a + 6\) , \( -a^{2} + 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 4\) , \( 8 a^{4} - 14 a^{3} - 38 a^{2} + 50 a + 25\) , \( -133 a^{4} + 179 a^{3} + 647 a^{2} - 642 a - 410\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+3a+6\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+7a+4\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(8a^{4}-14a^{3}-38a^{2}+50a+25\right){x}-133a^{4}+179a^{3}+647a^{2}-642a-410$ |
| 8.1-b1 |
8.1-b |
$6$ |
$8$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{8} \) |
$43.09176$ |
$(-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3788.666899$ |
1.20906538 |
\( 15076151280 a^{4} - 59809521632 a^{3} + 57350357056 a^{2} + 7791837048 a - 15327821088 \) |
\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 6 a + 4\) , \( a^{2} - 3\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 6 a^{4} - 11 a^{3} - 22 a^{2} + 40 a - 6\) , \( -11 a^{4} + 26 a^{3} + 34 a^{2} - 98 a + 38\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+6a+4\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(6a^{4}-11a^{3}-22a^{2}+40a-6\right){x}-11a^{4}+26a^{3}+34a^{2}-98a+38$ |
| 8.1-b2 |
8.1-b |
$6$ |
$8$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$43.09176$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$15154.66759$ |
1.20906538 |
\( 16384 a^{4} - 64000 a^{3} + 59456 a^{2} + 8320 a - 11520 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( a^{3} - 4 a - 2\) , \( a^{4} - 6 a^{2} - a + 6\) , \( a^{3} - a^{2} - 3 a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}{y}+\left(a^{4}-6a^{2}-a+6\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(a^{3}-a^{2}-3a+6\right){x}+a^{4}-a^{3}-3a^{2}+3a-5$ |
| 8.1-b3 |
8.1-b |
$6$ |
$8$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$43.09176$ |
$(-a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15154.66759$ |
1.20906538 |
\( 4096 a^{4} + 16416 a^{3} + 19328 a^{2} + 6272 a + 768 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -13 a^{4} + 43 a^{2} - 16 a - 3\) , \( 51 a^{4} + 16 a^{3} - 169 a^{2} + 17 a + 45\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-7a-2\right){x}^{2}+\left(-13a^{4}+43a^{2}-16a-3\right){x}+51a^{4}+16a^{3}-169a^{2}+17a+45$ |
| 8.1-b4 |
8.1-b |
$6$ |
$8$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$43.09176$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$947.1667249$ |
1.20906538 |
\( 1060880 a^{4} + 131008 a^{3} - 8224704 a^{2} - 1048568 a + 14877424 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( -a^{2} + a + 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 6 a + 4\) , \( 47 a^{4} - 115 a^{3} - 137 a^{2} + 434 a - 192\) , \( 385 a^{4} - 945 a^{3} - 1106 a^{2} + 3576 a - 1645\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+6a+4\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(47a^{4}-115a^{3}-137a^{2}+434a-192\right){x}+385a^{4}-945a^{3}-1106a^{2}+3576a-1645$ |
| 8.1-b5 |
8.1-b |
$6$ |
$8$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$43.09176$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$59.19792031$ |
1.20906538 |
\( -20745115763328 a^{4} + 51104670548994 a^{3} + 59313998842948 a^{2} - 193453364678416 a + 89597796481512 \) |
\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 4\) , \( a^{3} - a^{2} - 5 a + 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 6 a + 4\) , \( -4 a^{4} + 13 a^{3} - 9 a^{2} - 13 a + 3\) , \( -13 a^{4} + 55 a^{3} - 67 a^{2} - 13 a + 17\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+7a+4\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+6a+4\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+2\right){x}^{2}+\left(-4a^{4}+13a^{3}-9a^{2}-13a+3\right){x}-13a^{4}+55a^{3}-67a^{2}-13a+17$ |
| 8.1-b6 |
8.1-b |
$6$ |
$8$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{4} \) |
$43.09176$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$59.19792031$ |
1.20906538 |
\( 29921634845056 a^{4} - 40779260888066 a^{3} - 145741433324612 a^{2} + 146506905882384 a + 93685848669160 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 6 a - 4\) , \( a\) , \( -5 a^{3} - 4 a^{2} + 7 a - 6\) , \( -74 a^{4} - 43 a^{3} + 219 a^{2} - 68\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}{y}+a{y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-6a-4\right){x}^{2}+\left(-5a^{3}-4a^{2}+7a-6\right){x}-74a^{4}-43a^{3}+219a^{2}-68$ |
| 11.1-a1 |
11.1-a |
$4$ |
$6$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{9} \) |
$44.48611$ |
$(a^4-a^3-5a^2+4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$3.039803646$ |
$29.38954786$ |
2.56592707 |
\( -\frac{423331489660757591808}{2357947691} a^{4} + \frac{214963464836962382848}{2357947691} a^{3} + \frac{183026177372419272448}{214358881} a^{2} - \frac{381542596770911080064}{2357947691} a - \frac{565756924106837369088}{2357947691} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 2 a + 6\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 8 a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( -128 a^{4} + 151 a^{3} + 614 a^{2} - 544 a - 381\) , \( 55 a^{4} - 159 a^{3} - 334 a^{2} + 517 a + 275\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+2a+6\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+8a-3\right){x}^{2}+\left(-128a^{4}+151a^{3}+614a^{2}-544a-381\right){x}+55a^{4}-159a^{3}-334a^{2}+517a+275$ |
| 11.1-a2 |
11.1-a |
$4$ |
$6$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{6} \) |
$44.48611$ |
$(a^4-a^3-5a^2+4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.506633941$ |
$7141.660131$ |
2.56592707 |
\( -\frac{8362678256}{1771561} a^{4} + \frac{69732689824}{1771561} a^{3} + \frac{3127973312}{161051} a^{2} - \frac{229580899840}{1771561} a + \frac{75746089664}{1771561} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 2 a + 5\) , \( 4 a^{4} - 6 a^{3} - 19 a^{2} + 23 a + 11\) , \( 8 a^{4} - 8 a^{3} - 38 a^{2} + 25 a + 18\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+2a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){x}^{2}+\left(4a^{4}-6a^{3}-19a^{2}+23a+11\right){x}+8a^{4}-8a^{3}-38a^{2}+25a+18$ |
| 11.1-a3 |
11.1-a |
$4$ |
$6$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{18} \) |
$44.48611$ |
$(a^4-a^3-5a^2+4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1.519901823$ |
$29.38954786$ |
2.56592707 |
\( \frac{1931270407547241143496464}{5559917313492231481} a^{4} - \frac{3877359867428167210964448}{5559917313492231481} a^{3} - \frac{176790441605569148158528}{505447028499293771} a^{2} + \frac{1260426851406435226365184}{5559917313492231481} a + \frac{691266819800971589478208}{5559917313492231481} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 2 a + 5\) , \( 19 a^{4} - 11 a^{3} - 104 a^{2} + 53 a + 31\) , \( 49 a^{4} - 14 a^{3} - 286 a^{2} + 99 a + 83\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+2a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){x}^{2}+\left(19a^{4}-11a^{3}-104a^{2}+53a+31\right){x}+49a^{4}-14a^{3}-286a^{2}+99a+83$ |
| 11.1-a4 |
11.1-a |
$4$ |
$6$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$44.48611$ |
$(a^4-a^3-5a^2+4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1.013267882$ |
$7141.660131$ |
2.56592707 |
\( \frac{179756979456}{1331} a^{4} - \frac{244473870336}{1331} a^{3} - \frac{79589738240}{121} a^{2} + \frac{877765531008}{1331} a + \frac{561759070976}{1331} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 2 a + 6\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 8 a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( -98 a^{4} + 126 a^{3} + 474 a^{2} - 444 a - 281\) , \( 527 a^{4} - 729 a^{3} - 2568 a^{2} + 2629 a + 1668\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+2a+6\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+8a-3\right){x}^{2}+\left(-98a^{4}+126a^{3}+474a^{2}-444a-281\right){x}+527a^{4}-729a^{3}-2568a^{2}+2629a+1668$ |
| 11.1-b1 |
11.1-b |
$4$ |
$10$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$44.48611$ |
$(a^4-a^3-5a^2+4a+1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$13492.86057$ |
0.688949482 |
\( \frac{13663888}{121} a^{4} - \frac{52550048}{121} a^{3} + \frac{4514176}{11} a^{2} + \frac{6322944}{121} a - \frac{12952000}{121} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( -a^{2} + a + 4\) , \( -a^{4} + 5 a^{2} - 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-3\right){x}^{2}+\left(-a^{2}+a+4\right){x}-a^{4}+5a^{2}-4$ |
| 11.1-b2 |
11.1-b |
$4$ |
$10$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$44.48611$ |
$(a^4-a^3-5a^2+4a+1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$26985.72114$ |
0.688949482 |
\( \frac{2553856}{11} a^{4} - \frac{3456000}{11} a^{3} - 1133824 a^{2} + \frac{12412288}{11} a + \frac{8108288}{11} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 2 a + 6\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( -13 a^{4} + 6 a^{3} + 62 a^{2} - 8 a - 20\) , \( -21 a^{4} + 8 a^{3} + 105 a^{2} - 15 a - 32\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+2a+6\right){x}{y}+\left(a^{3}-a^{2}-4a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-1\right){x}^{2}+\left(-13a^{4}+6a^{3}+62a^{2}-8a-20\right){x}-21a^{4}+8a^{3}+105a^{2}-15a-32$ |
| 11.1-b3 |
11.1-b |
$4$ |
$10$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{5} \) |
$44.48611$ |
$(a^4-a^3-5a^2+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 5 \) |
$1$ |
$8.635430766$ |
0.688949482 |
\( \frac{44749691639973028352}{161051} a^{4} + \frac{13337652081702171648}{161051} a^{3} - \frac{13489617835720488192}{14641} a^{2} + \frac{16932506423664741760}{161051} a + \frac{38936427535157859584}{161051} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 2 a + 6\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( 137 a^{4} - 64 a^{3} - 658 a^{2} + 122 a + 150\) , \( 2331 a^{4} - 1083 a^{3} - 11305 a^{2} + 2091 a + 3076\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+2a+6\right){x}{y}+\left(a^{3}-a^{2}-4a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-1\right){x}^{2}+\left(137a^{4}-64a^{3}-658a^{2}+122a+150\right){x}+2331a^{4}-1083a^{3}-11305a^{2}+2091a+3076$ |
| 11.1-b4 |
11.1-b |
$4$ |
$10$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$44.48611$ |
$(a^4-a^3-5a^2+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \cdot 5 \) |
$1$ |
$4.317715383$ |
0.688949482 |
\( -\frac{4405849200982986067119108976}{25937424601} a^{4} + \frac{10852207348875307893128617952}{25937424601} a^{3} + \frac{1145213184689328820277206528}{2357947691} a^{2} - \frac{41081082089468374348527507712}{25937424601} a + \frac{19026142683497043770919919168}{25937424601} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 4\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( -49 a^{4} + 66 a^{3} + 155 a^{2} - 155 a - 99\) , \( -343 a^{4} + 522 a^{3} + 1076 a^{2} - 1169 a - 708\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-7a-4\right){x}^{2}+\left(-49a^{4}+66a^{3}+155a^{2}-155a-99\right){x}-343a^{4}+522a^{3}+1076a^{2}-1169a-708$ |
| 14.1-a1 |
14.1-a |
$1$ |
$1$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{6} \) |
$45.57199$ |
$(-a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$447.5042436$ |
2.28497000 |
\( -\frac{1303525154581}{235298} a^{4} + \frac{879152126897}{117649} a^{3} + \frac{3166857320210}{117649} a^{2} - \frac{3164438444278}{117649} a - \frac{2027455120538}{117649} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a\) , \( a^{4} - 5 a^{2} - a + 2\) , \( -56 a^{4} + 137 a^{3} + 162 a^{2} - 519 a + 235\) , \( 539 a^{4} - 1325 a^{3} - 1543 a^{2} + 5014 a - 2323\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+3\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a\right){x}^{2}+\left(-56a^{4}+137a^{3}+162a^{2}-519a+235\right){x}+539a^{4}-1325a^{3}-1543a^{2}+5014a-2323$ |
| 14.1-b1 |
14.1-b |
$1$ |
$1$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{15} \cdot 7^{2} \) |
$45.57199$ |
$(-a), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.003208590$ |
$3991.459954$ |
4.90445427 |
\( -\frac{76186529}{392} a^{4} + \frac{52231685}{196} a^{3} + \frac{184249985}{196} a^{2} - \frac{185421137}{196} a - \frac{236921225}{392} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 9 a\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a\) , \( -3 a^{4} + 4 a^{3} + 15 a^{2} - 16 a - 6\) , \( 3 a^{3} - 4 a^{2} - 14 a + 16\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+9a\right){x}^{2}+\left(-3a^{4}+4a^{3}+15a^{2}-16a-6\right){x}+3a^{3}-4a^{2}-14a+16$ |
| 16.1-a1 |
16.1-a |
$6$ |
$8$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$46.18460$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$780.7300804$ |
1.99321553 |
\( 15076151280 a^{4} - 59809521632 a^{3} + 57350357056 a^{2} + 7791837048 a - 15327821088 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( -3 a^{4} + a^{3} + 13 a^{2} - 1\) , \( -2 a^{3} - a^{2} + 10 a + 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-3\right){x}^{2}+\left(-3a^{4}+a^{3}+13a^{2}-1\right){x}-2a^{3}-a^{2}+10a+3$ |
| 16.1-a2 |
16.1-a |
$6$ |
$8$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$46.18460$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$12491.68128$ |
1.99321553 |
\( 16384 a^{4} - 64000 a^{3} + 59456 a^{2} + 8320 a - 11520 \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 2 a + 6\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 4\) , \( -2 a^{4} - 11 a^{3} + 22 a^{2} + 51 a - 45\) , \( -33 a^{4} + 61 a^{3} + 113 a^{2} - 217 a + 77\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+2a+6\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+7a+4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-2a^{4}-11a^{3}+22a^{2}+51a-45\right){x}-33a^{4}+61a^{3}+113a^{2}-217a+77$ |
| 16.1-a3 |
16.1-a |
$6$ |
$8$ |
5.5.153424.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$46.18460$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3122.920321$ |
1.99321553 |
\( 4096 a^{4} + 16416 a^{3} + 19328 a^{2} + 6272 a + 768 \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 2 a + 6\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( -9 a^{4} + 7 a^{3} + 42 a^{2} - 20 a - 12\) , \( -8 a^{4} + 6 a^{3} + 37 a^{2} - 16 a - 10\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+2a+6\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-2\right){x}^{2}+\left(-9a^{4}+7a^{3}+42a^{2}-20a-12\right){x}-8a^{4}+6a^{3}+37a^{2}-16a-10$ |
*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.
