| 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 |
| 7.1-a1 |
7.1-a |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$16$ |
\( 1 \) |
$1$ |
$26.92358280$ |
0.899453772 |
\( \frac{602901386081720}{49} a^{3} + 28616995979968 a^{2} - \frac{1559424228748496}{49} a - 73982672348408 \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( 4 a^{3} + 25 a^{2} - 34 a - 165\) , \( 523 a^{3} + 906 a^{2} - 2882 a - 5023\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(4a^{3}+25a^{2}-34a-165\right){x}+523a^{3}+906a^{2}-2882a-5023$ |
| 7.1-a2 |
7.1-a |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 1 \) |
$1$ |
$107.6943312$ |
0.899453772 |
\( -\frac{602901386081720}{49} a^{3} + 28616995979968 a^{2} + \frac{1559424228748496}{49} a - 73982672348408 \) |
\( \bigl[a^{3} - 5 a\) , \( -a^{2} + a + 4\) , \( a^{3} - 5 a + 1\) , \( 580 a^{3} + 936 a^{2} - 3142 a - 5068\) , \( 17634 a^{3} + 28360 a^{2} - 95475 a - 153550\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(580a^{3}+936a^{2}-3142a-5068\right){x}+17634a^{3}+28360a^{2}-95475a-153550$ |
| 7.1-a3 |
7.1-a |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$4$ |
\( 2 \) |
$1$ |
$215.3886624$ |
0.899453772 |
\( \frac{1522238080}{343} a^{2} - \frac{3876979392}{343} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{2} - 4\) , \( 1\) , \( 17 a^{3} - 38 a^{2} - 37 a + 90\) , \( -101 a^{3} + 236 a^{2} + 269 a - 623\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(17a^{3}-38a^{2}-37a+90\right){x}-101a^{3}+236a^{2}+269a-623$ |
| 7.1-a4 |
7.1-a |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{12} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$215.3886624$ |
0.899453772 |
\( -\frac{193336704}{117649} a^{2} + \frac{708330176}{117649} \) |
\( \bigl[a^{2} - 4\) , \( -a\) , \( a^{2} + a - 3\) , \( 3 a^{3} - 9 a^{2} - 5 a + 20\) , \( -13 a^{3} + 28 a^{2} + 35 a - 75\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}-a{x}^{2}+\left(3a^{3}-9a^{2}-5a+20\right){x}-13a^{3}+28a^{2}+35a-75$ |
| 7.1-b1 |
7.1-b |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.112729255$ |
$2441.990990$ |
2.299146793 |
\( \frac{951050008}{7} a^{3} + 345751616 a^{2} - \frac{1643478080}{7} a - 706649592 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - 3\) , \( 6 a^{3} - 19 a^{2} - 13 a + 53\) , \( -10 a^{3} + 21 a^{2} + 27 a - 52\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(6a^{3}-19a^{2}-13a+53\right){x}-10a^{3}+21a^{2}+27a-52$ |
| 7.1-b2 |
7.1-b |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.450917022$ |
$610.4977476$ |
2.299146793 |
\( -\frac{951050008}{7} a^{3} + 345751616 a^{2} + \frac{1643478080}{7} a - 706649592 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( 0\) , \( a + 1\) , \( 52 a^{3} - 133 a^{2} - 125 a + 352\) , \( 580 a^{3} - 1355 a^{2} - 1498 a + 3512\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(52a^{3}-133a^{2}-125a+352\right){x}+580a^{3}-1355a^{2}-1498a+3512$ |
| 7.1-b3 |
7.1-b |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.225458511$ |
$2441.990990$ |
2.299146793 |
\( \frac{71552}{7} a^{2} - \frac{44224}{7} \) |
\( \bigl[a^{2} - 4\) , \( -a^{3} + a^{2} + 6 a - 5\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 6 a^{3} + 2 a^{2} - 33 a - 13\) , \( -6 a^{3} - 4 a^{2} + 32 a + 20\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-5\right){x}^{2}+\left(6a^{3}+2a^{2}-33a-13\right){x}-6a^{3}-4a^{2}+32a+20$ |
| 7.1-b4 |
7.1-b |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.112729255$ |
$610.4977476$ |
2.299146793 |
\( -\frac{65664}{49} a^{2} + \frac{355520}{49} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - 4 a + 1\) , \( 1\) , \( 5 a^{3} + 9 a^{2} - 21 a - 33\) , \( 9 a^{3} + 16 a^{2} - 41 a - 69\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(5a^{3}+9a^{2}-21a-33\right){x}+9a^{3}+16a^{2}-41a-69$ |
| 7.1-c1 |
7.1-c |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.450917022$ |
$610.4977476$ |
2.299146793 |
\( \frac{951050008}{7} a^{3} + 345751616 a^{2} - \frac{1643478080}{7} a - 706649592 \) |
\( \bigl[a^{2} + a - 4\) , \( a - 1\) , \( a^{2} + a - 3\) , \( 30 a^{3} + 49 a^{2} - 168 a - 275\) , \( -212 a^{3} - 345 a^{2} + 1132 a + 1830\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(30a^{3}+49a^{2}-168a-275\right){x}-212a^{3}-345a^{2}+1132a+1830$ |
| 7.1-c2 |
7.1-c |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.112729255$ |
$2441.990990$ |
2.299146793 |
\( -\frac{951050008}{7} a^{3} + 345751616 a^{2} + \frac{1643478080}{7} a - 706649592 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a + 1\) , \( a^{2} + a - 3\) , \( -2 a^{3} - 5 a^{2} + 11 a + 29\) , \( -16 a^{3} - 26 a^{2} + 86 a + 139\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(-2a^{3}-5a^{2}+11a+29\right){x}-16a^{3}-26a^{2}+86a+139$ |
| 7.1-c3 |
7.1-c |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.225458511$ |
$2441.990990$ |
2.299146793 |
\( \frac{71552}{7} a^{2} - \frac{44224}{7} \) |
\( \bigl[a^{2} - 4\) , \( -a^{3} - a^{2} + 5 a + 3\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 7 a^{3} - 18 a^{2} - 18 a + 51\) , \( -28 a^{3} + 64 a^{2} + 73 a - 167\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+3\right){x}^{2}+\left(7a^{3}-18a^{2}-18a+51\right){x}-28a^{3}+64a^{2}+73a-167$ |
| 7.1-c4 |
7.1-c |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.112729255$ |
$610.4977476$ |
2.299146793 |
\( -\frac{65664}{49} a^{2} + \frac{355520}{49} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - a^{2} - 6 a + 5\) , \( a^{3} - 4 a + 1\) , \( 2 a^{3} - 4 a^{2} - 12 a + 19\) , \( -8 a^{3} + 19 a^{2} + 16 a - 42\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+5\right){x}^{2}+\left(2a^{3}-4a^{2}-12a+19\right){x}-8a^{3}+19a^{2}+16a-42$ |
| 7.1-d1 |
7.1-d |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 1 \) |
$1$ |
$107.6943312$ |
0.899453772 |
\( \frac{602901386081720}{49} a^{3} + 28616995979968 a^{2} - \frac{1559424228748496}{49} a - 73982672348408 \) |
\( \bigl[a\) , \( a^{3} - 4 a - 1\) , \( a^{3} - 4 a + 1\) , \( -8 a^{3} + a^{2} + 69 a - 77\) , \( -69 a^{3} + 93 a^{2} + 443 a - 667\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(-8a^{3}+a^{2}+69a-77\right){x}-69a^{3}+93a^{2}+443a-667$ |
| 7.1-d2 |
7.1-d |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$16$ |
\( 1 \) |
$1$ |
$26.92358280$ |
0.899453772 |
\( -\frac{602901386081720}{49} a^{3} + 28616995979968 a^{2} + \frac{1559424228748496}{49} a - 73982672348408 \) |
\( \bigl[a^{3} - 5 a\) , \( a^{3} - 4 a + 1\) , \( a + 1\) , \( 151 a^{3} - 351 a^{2} - 393 a + 917\) , \( 2456 a^{3} - 5715 a^{2} - 6345 a + 14765\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(151a^{3}-351a^{2}-393a+917\right){x}+2456a^{3}-5715a^{2}-6345a+14765$ |
| 7.1-d3 |
7.1-d |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$4$ |
\( 2 \) |
$1$ |
$215.3886624$ |
0.899453772 |
\( \frac{1522238080}{343} a^{2} - \frac{3876979392}{343} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} - a^{2} + 6 a + 3\) , \( a^{2} - 3\) , \( 69 a^{3} + 112 a^{2} - 376 a - 607\) , \( 942 a^{3} + 1514 a^{2} - 5100 a - 8199\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+3\right){x}^{2}+\left(69a^{3}+112a^{2}-376a-607\right){x}+942a^{3}+1514a^{2}-5100a-8199$ |
| 7.1-d4 |
7.1-d |
$4$ |
$4$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{12} \) |
$13.64551$ |
$(a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$215.3886624$ |
0.899453772 |
\( -\frac{193336704}{117649} a^{2} + \frac{708330176}{117649} \) |
\( \bigl[a^{2} - 4\) , \( a^{3} - a^{2} - 4 a + 5\) , \( a + 1\) , \( 29 a^{3} + 46 a^{2} - 158 a - 247\) , \( -22 a^{3} - 36 a^{2} + 119 a + 193\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+5\right){x}^{2}+\left(29a^{3}+46a^{2}-158a-247\right){x}-22a^{3}-36a^{2}+119a+193$ |
| 8.1-a1 |
8.1-a |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.87519$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$537.2089925$ |
2.243361601 |
\( 3694464 a^{3} + 8581440 a^{2} - 9563840 a - 22169696 \) |
\( \bigl[a^{2} - 4\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 2 a^{3} - 4 a^{2} - 7 a + 11\) , \( 5 a^{3} - 3 a^{2} - 19 a - 4\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(2a^{3}-4a^{2}-7a+11\right){x}+5a^{3}-3a^{2}-19a-4$ |
| 8.1-a2 |
8.1-a |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.87519$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$268.6044962$ |
2.243361601 |
\( -235008 a^{3} + 549120 a^{2} + 608000 a - 1419392 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 5 a\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -2 a^{3} - 8 a^{2} + 6 a + 30\) , \( -a^{3} - 7 a^{2} - 8 a + 6\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-2a^{3}-8a^{2}+6a+30\right){x}-a^{3}-7a^{2}-8a+6$ |
| 8.1-b1 |
8.1-b |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.87519$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.088486702$ |
$1799.850408$ |
2.660298815 |
\( -3694464 a^{3} + 8581440 a^{2} + 9563840 a - 22169696 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - 4 a - 1\) , \( a\) , \( 7 a^{3} + 12 a^{2} - 35 a - 57\) , \( 19 a^{3} + 31 a^{2} - 99 a - 161\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(7a^{3}+12a^{2}-35a-57\right){x}+19a^{3}+31a^{2}-99a-161$ |
| 8.1-b2 |
8.1-b |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.87519$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.176973404$ |
$899.9252042$ |
2.660298815 |
\( 235008 a^{3} + 549120 a^{2} - 608000 a - 1419392 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} - a^{2} + 6 a + 5\) , \( a^{2} - 4\) , \( -3 a^{3} - 5 a^{2} + 16 a + 29\) , \( 3 a^{3} + 5 a^{2} - 16 a - 27\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+5\right){x}^{2}+\left(-3a^{3}-5a^{2}+16a+29\right){x}+3a^{3}+5a^{2}-16a-27$ |
| 8.1-c1 |
8.1-c |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.87519$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$537.2089925$ |
2.243361601 |
\( -3694464 a^{3} + 8581440 a^{2} + 9563840 a - 22169696 \) |
\( \bigl[a^{2} - 4\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -a^{3} - 4 a^{2} + a + 11\) , \( -4 a^{3} - 3 a^{2} + 13 a - 4\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-a^{3}-4a^{2}+a+11\right){x}-4a^{3}-3a^{2}+13a-4$ |
| 8.1-c2 |
8.1-c |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.87519$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$268.6044962$ |
2.243361601 |
\( 235008 a^{3} + 549120 a^{2} - 608000 a - 1419392 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} - a^{2} + 6 a + 4\) , \( a^{3} + a^{2} - 4 a - 4\) , \( 53 a^{3} - 133 a^{2} - 132 a + 354\) , \( 498 a^{3} - 1168 a^{2} - 1282 a + 3028\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+4\right){x}^{2}+\left(53a^{3}-133a^{2}-132a+354\right){x}+498a^{3}-1168a^{2}-1282a+3028$ |
| 8.1-d1 |
8.1-d |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.87519$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.088486702$ |
$1799.850408$ |
2.660298815 |
\( 3694464 a^{3} + 8581440 a^{2} - 9563840 a - 22169696 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} + 5 a - 1\) , \( a^{3} - 5 a\) , \( -6 a^{3} + 8 a^{2} + 33 a - 43\) , \( -9 a^{3} + 13 a^{2} + 49 a - 70\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{3}+5a-1\right){x}^{2}+\left(-6a^{3}+8a^{2}+33a-43\right){x}-9a^{3}+13a^{2}+49a-70$ |
| 8.1-d2 |
8.1-d |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.87519$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.176973404$ |
$899.9252042$ |
2.660298815 |
\( -235008 a^{3} + 549120 a^{2} + 608000 a - 1419392 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 6 a + 5\) , \( a^{2} - 4\) , \( 3 a^{3} - 5 a^{2} - 18 a + 29\) , \( -3 a^{3} + 5 a^{2} + 16 a - 27\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+5\right){x}^{2}+\left(3a^{3}-5a^{2}-18a+29\right){x}-3a^{3}+5a^{2}+16a-27$ |
| 14.1-a1 |
14.1-a |
$1$ |
$1$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{9} \cdot 7^{3} \) |
$14.88054$ |
$(a-2), (a^3+2a^2-4a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$211.5083619$ |
1.766499609 |
\( -\frac{20028181}{392} a^{3} + \frac{833330}{7} a^{2} + \frac{25900853}{196} a - \frac{8620707}{28} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{2} + a - 3\) , \( -3 a^{2} + 12\) , \( 2 a^{3} - 6 a^{2} - 9 a + 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(-3a^{2}+12\right){x}+2a^{3}-6a^{2}-9a+24$ |
| 14.1-b1 |
14.1-b |
$1$ |
$1$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{9} \cdot 7^{3} \) |
$14.88054$ |
$(a-2), (a^3+2a^2-4a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$211.5083619$ |
1.766499609 |
\( \frac{20028181}{392} a^{3} + \frac{833330}{7} a^{2} - \frac{25900853}{196} a - \frac{8620707}{28} \) |
\( \bigl[a + 1\) , \( a^{3} + a^{2} - 6 a - 4\) , \( a^{2} + a - 3\) , \( -a^{3} - 3 a^{2} + 2 a + 12\) , \( -3 a^{3} - 6 a^{2} + 12 a + 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-4\right){x}^{2}+\left(-a^{3}-3a^{2}+2a+12\right){x}-3a^{3}-6a^{2}+12a+24$ |
| 14.1-c1 |
14.1-c |
$1$ |
$1$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{9} \cdot 7^{3} \) |
$14.88054$ |
$(a-2), (a^3+2a^2-4a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \) |
$0.020778315$ |
$599.9270325$ |
3.747980129 |
\( \frac{20028181}{392} a^{3} + \frac{833330}{7} a^{2} - \frac{25900853}{196} a - \frac{8620707}{28} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 6 a\) , \( a^{3} - 4 a\) , \( -2 a^{3} + a^{2} + 3 a + 11\) , \( -9 a^{3} + 24 a^{2} + 20 a - 63\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-6a\right){x}^{2}+\left(-2a^{3}+a^{2}+3a+11\right){x}-9a^{3}+24a^{2}+20a-63$ |
| 14.1-d1 |
14.1-d |
$1$ |
$1$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{9} \cdot 7^{3} \) |
$14.88054$ |
$(a-2), (a^3+2a^2-4a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \) |
$0.020778315$ |
$599.9270325$ |
3.747980129 |
\( -\frac{20028181}{392} a^{3} + \frac{833330}{7} a^{2} + \frac{25900853}{196} a - \frac{8620707}{28} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 6 a\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 3 a^{3} + a^{2} - 9 a + 12\) , \( 16 a^{3} + 32 a^{2} - 50 a - 88\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(a^{3}-6a\right){x}^{2}+\left(3a^{3}+a^{2}-9a+12\right){x}+16a^{3}+32a^{2}-50a-88$ |
| 14.2-a1 |
14.2-a |
$1$ |
$1$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{11} \cdot 7 \) |
$14.88054$ |
$(a-2), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 11 \) |
$0.019063074$ |
$660.5166573$ |
4.627169497 |
\( \frac{42731}{28} a^{3} - \frac{109775}{56} a^{2} - \frac{67765}{8} a + \frac{44469}{4} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{2} - a + 3\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 6 a - 1\) , \( a^{3} - 2 a^{2} - 5 a + 7\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(a^{3}+a^{2}-6a-1\right){x}+a^{3}-2a^{2}-5a+7$ |
| 14.2-b1 |
14.2-b |
$2$ |
$7$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{7} \cdot 7^{7} \) |
$14.88054$ |
$(a-2), (a-1)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$397.7201662$ |
3.321724549 |
\( \frac{33023986113}{3294172} a^{3} - \frac{68284593133}{3294172} a^{2} - \frac{27111731323}{470596} a + \frac{12301174505}{117649} \) |
\( \bigl[a^{2} - 3\) , \( -a - 1\) , \( a + 1\) , \( -8 a^{3} - 14 a^{2} + 33 a + 56\) , \( -520 a^{3} - 829 a^{2} + 2843 a + 4553\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a^{3}-14a^{2}+33a+56\right){x}-520a^{3}-829a^{2}+2843a+4553$ |
| 14.2-b2 |
14.2-b |
$2$ |
$7$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7 \) |
$14.88054$ |
$(a-2), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.165647716$ |
3.321724549 |
\( \frac{166950469459413024051452605392780049}{14} a^{3} - \frac{134231355426915602479576891671325693}{7} a^{2} - 64564678285122085494945101931307232 a + 103822460721161401268292562311544755 \) |
\( \bigl[a^{2} - 3\) , \( -a - 1\) , \( a + 1\) , \( 8197 a^{3} + 13146 a^{2} - 44572 a - 71624\) , \( 866109 a^{3} + 1391730 a^{2} - 4693395 a - 7544667\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(8197a^{3}+13146a^{2}-44572a-71624\right){x}+866109a^{3}+1391730a^{2}-4693395a-7544667$ |
| 14.2-c1 |
14.2-c |
$2$ |
$7$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{7} \cdot 7^{7} \) |
$14.88054$ |
$(a-2), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$85.91782318$ |
0.717578254 |
\( \frac{33023986113}{3294172} a^{3} - \frac{68284593133}{3294172} a^{2} - \frac{27111731323}{470596} a + \frac{12301174505}{117649} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{2} - 5\) , \( 0\) , \( 2 a^{2} + a - 5\) , \( -a^{2} + 2 a + 5\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(2a^{2}+a-5\right){x}-a^{2}+2a+5$ |
| 14.2-c2 |
14.2-c |
$2$ |
$7$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7 \) |
$14.88054$ |
$(a-2), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$1.753424963$ |
0.717578254 |
\( \frac{166950469459413024051452605392780049}{14} a^{3} - \frac{134231355426915602479576891671325693}{7} a^{2} - 64564678285122085494945101931307232 a + 103822460721161401268292562311544755 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 6 a + 1\) , \( a^{3} - 5 a\) , \( 3101 a^{3} - 7265 a^{2} - 8000 a + 18727\) , \( -240709 a^{3} + 560496 a^{2} + 622612 a - 1449661\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(a^{3}-6a+1\right){x}^{2}+\left(3101a^{3}-7265a^{2}-8000a+18727\right){x}-240709a^{3}+560496a^{2}+622612a-1449661$ |
| 14.2-d1 |
14.2-d |
$1$ |
$1$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{11} \cdot 7 \) |
$14.88054$ |
$(a-2), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.111658587$ |
$505.3719494$ |
1.885164520 |
\( \frac{42731}{28} a^{3} - \frac{109775}{56} a^{2} - \frac{67765}{8} a + \frac{44469}{4} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 5 a - 5\) , \( a^{2} - 4\) , \( 4 a^{3} + 3 a^{2} - 22 a - 15\) , \( -9 a^{3} - 12 a^{2} + 48 a + 63\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-5\right){x}^{2}+\left(4a^{3}+3a^{2}-22a-15\right){x}-9a^{3}-12a^{2}+48a+63$ |
| 14.3-a1 |
14.3-a |
$1$ |
$1$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{11} \cdot 7 \) |
$14.88054$ |
$(a-2), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 11 \) |
$0.019063074$ |
$660.5166573$ |
4.627169497 |
\( -\frac{42731}{28} a^{3} - \frac{109775}{56} a^{2} + \frac{67765}{8} a + \frac{44469}{4} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} - a^{2} + 6 a + 3\) , \( a^{3} - 5 a + 1\) , \( -3 a^{3} + a^{2} + 16 a - 1\) , \( -2 a^{3} - 2 a^{2} + 10 a + 7\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+3\right){x}^{2}+\left(-3a^{3}+a^{2}+16a-1\right){x}-2a^{3}-2a^{2}+10a+7$ |
| 14.3-b1 |
14.3-b |
$2$ |
$7$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{7} \cdot 7^{7} \) |
$14.88054$ |
$(a-2), (-a-1)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$397.7201662$ |
3.321724549 |
\( -\frac{33023986113}{3294172} a^{3} - \frac{68284593133}{3294172} a^{2} + \frac{27111731323}{470596} a + \frac{12301174505}{117649} \) |
\( \bigl[a^{2} - 3\) , \( a - 1\) , \( a + 1\) , \( 7 a^{3} - 14 a^{2} - 30 a + 56\) , \( 520 a^{3} - 829 a^{2} - 2844 a + 4553\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a^{3}-14a^{2}-30a+56\right){x}+520a^{3}-829a^{2}-2844a+4553$ |
| 14.3-b2 |
14.3-b |
$2$ |
$7$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7 \) |
$14.88054$ |
$(a-2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.165647716$ |
3.321724549 |
\( -\frac{166950469459413024051452605392780049}{14} a^{3} - \frac{134231355426915602479576891671325693}{7} a^{2} + 64564678285122085494945101931307232 a + 103822460721161401268292562311544755 \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{2} - 3\) , \( 2040 a^{3} - 5005 a^{2} - 4587 a + 11836\) , \( 295481 a^{3} - 691043 a^{2} - 752116 a + 1767697\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(2040a^{3}-5005a^{2}-4587a+11836\right){x}+295481a^{3}-691043a^{2}-752116a+1767697$ |
| 14.3-c1 |
14.3-c |
$2$ |
$7$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{7} \cdot 7^{7} \) |
$14.88054$ |
$(a-2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$85.91782318$ |
0.717578254 |
\( -\frac{33023986113}{3294172} a^{3} - \frac{68284593133}{3294172} a^{2} + \frac{27111731323}{470596} a + \frac{12301174505}{117649} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a - 5\) , \( 0\) , \( 2 a^{2} - a - 5\) , \( -a^{2} - 2 a + 5\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-5\right){x}^{2}+\left(2a^{2}-a-5\right){x}-a^{2}-2a+5$ |
| 14.3-c2 |
14.3-c |
$2$ |
$7$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7 \) |
$14.88054$ |
$(a-2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$1.753424963$ |
0.717578254 |
\( -\frac{166950469459413024051452605392780049}{14} a^{3} - \frac{134231355426915602479576891671325693}{7} a^{2} + 64564678285122085494945101931307232 a + 103822460721161401268292562311544755 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a - 5\) , \( 0\) , \( 195 a^{3} + 562 a^{2} - 1316 a - 3645\) , \( 8905 a^{3} + 18563 a^{2} - 44887 a - 92759\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-5\right){x}^{2}+\left(195a^{3}+562a^{2}-1316a-3645\right){x}+8905a^{3}+18563a^{2}-44887a-92759$ |
| 14.3-d1 |
14.3-d |
$1$ |
$1$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{11} \cdot 7 \) |
$14.88054$ |
$(a-2), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.111658587$ |
$505.3719494$ |
1.885164520 |
\( -\frac{42731}{28} a^{3} - \frac{109775}{56} a^{2} + \frac{67765}{8} a + \frac{44469}{4} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{2} - a + 4\) , \( a^{3} - 5 a + 1\) , \( -3 a^{3} + 6 a^{2} + 7 a - 14\) , \( 65 a^{3} - 152 a^{2} - 168 a + 394\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-3a^{3}+6a^{2}+7a-14\right){x}+65a^{3}-152a^{2}-168a+394$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$15.13100$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.085976041$ |
$3628.121456$ |
2.605225186 |
\( -3694464 a^{3} + 8581440 a^{2} + 9563840 a - 22169696 \) |
\( \bigl[a^{2} - 4\) , \( -a^{3} + 5 a + 1\) , \( a\) , \( -4 a^{3} - 4 a^{2} + 16 a + 12\) , \( 2 a^{3} - 7 a + 8\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-4a^{3}-4a^{2}+16a+12\right){x}+2a^{3}-7a+8$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.13100$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.171952083$ |
$1814.060728$ |
2.605225186 |
\( 235008 a^{3} + 549120 a^{2} - 608000 a - 1419392 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 6 a - 1\) , \( a^{2} - 4\) , \( 55 a^{3} - 131 a^{2} - 144 a + 349\) , \( -444 a^{3} + 1036 a^{2} + 1144 a - 2678\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(55a^{3}-131a^{2}-144a+349\right){x}-444a^{3}+1036a^{2}+1144a-2678$ |
| 16.1-b1 |
16.1-b |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$15.13100$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.392781584$ |
$1082.900813$ |
3.552432229 |
\( 3694464 a^{3} + 8581440 a^{2} - 9563840 a - 22169696 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{2} + a - 4\) , \( -6 a^{3} + 11 a^{2} + 32 a - 54\) , \( 12 a^{3} - 18 a^{2} - 63 a + 98\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(-6a^{3}+11a^{2}+32a-54\right){x}+12a^{3}-18a^{2}-63a+98$ |
| 16.1-b2 |
16.1-b |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.13100$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.785563168$ |
$541.4504069$ |
3.552432229 |
\( -235008 a^{3} + 549120 a^{2} + 608000 a - 1419392 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + 6 a + 1\) , \( a^{2} - 4\) , \( -a^{3} - 3 a^{2} + 6 a + 21\) , \( 5 a^{3} - 13 a^{2} - 26 a + 72\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{3}+6a+1\right){x}^{2}+\left(-a^{3}-3a^{2}+6a+21\right){x}+5a^{3}-13a^{2}-26a+72$ |
| 16.1-c1 |
16.1-c |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$15.13100$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.085976041$ |
$3628.121456$ |
2.605225186 |
\( 3694464 a^{3} + 8581440 a^{2} - 9563840 a - 22169696 \) |
\( \bigl[a^{2} - 4\) , \( a^{3} - 5 a + 1\) , \( a\) , \( 3 a^{3} - 4 a^{2} - 12 a + 12\) , \( -2 a^{3} + 7 a + 8\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(3a^{3}-4a^{2}-12a+12\right){x}-2a^{3}+7a+8$ |
| 16.1-c2 |
16.1-c |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.13100$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.171952083$ |
$1814.060728$ |
2.605225186 |
\( -235008 a^{3} + 549120 a^{2} + 608000 a - 1419392 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} - a^{2} + 5 a + 3\) , \( a^{2} - 4\) , \( -4 a^{3} - 8 a^{2} + 16 a + 33\) , \( -2 a^{3} - a^{2} + 19 a + 24\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+3\right){x}^{2}+\left(-4a^{3}-8a^{2}+16a+33\right){x}-2a^{3}-a^{2}+19a+24$ |
| 16.1-d1 |
16.1-d |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$15.13100$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.392781584$ |
$1082.900813$ |
3.552432229 |
\( -3694464 a^{3} + 8581440 a^{2} + 9563840 a - 22169696 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} - a^{2} + 5 a + 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 5 a^{3} + 7 a^{2} - 28 a - 40\) , \( -3 a^{3} - 4 a^{2} + 16 a + 21\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+3\right){x}^{2}+\left(5a^{3}+7a^{2}-28a-40\right){x}-3a^{3}-4a^{2}+16a+21$ |
| 16.1-d2 |
16.1-d |
$2$ |
$2$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.13100$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.785563168$ |
$541.4504069$ |
3.552432229 |
\( 235008 a^{3} + 549120 a^{2} - 608000 a - 1419392 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 6 a + 1\) , \( a^{2} - 4\) , \( a^{3} - 3 a^{2} - 8 a + 21\) , \( -5 a^{3} - 13 a^{2} + 26 a + 72\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{3}-6a+1\right){x}^{2}+\left(a^{3}-3a^{2}-8a+21\right){x}-5a^{3}-13a^{2}+26a+72$ |
| 28.1-a1 |
28.1-a |
$8$ |
$12$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{12} \) |
$16.22734$ |
$(a-2), (a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$138.1047704$ |
2.595238063 |
\( \frac{1137747277344}{117649} a^{2} - \frac{2928602491408}{117649} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - 5 a - 1\) , \( a^{2} - 4\) , \( -520 a^{3} + 612 a^{2} + 2654 a - 3690\) , \( -11466 a^{3} + 20429 a^{2} + 63510 a - 107276\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(-520a^{3}+612a^{2}+2654a-3690\right){x}-11466a^{3}+20429a^{2}+63510a-107276$ |
| 28.1-a2 |
28.1-a |
$8$ |
$12$ |
4.4.14336.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{4} \) |
$16.22734$ |
$(a-2), (a^3+2a^2-4a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1242.942933$ |
2.595238063 |
\( -\frac{435744}{49} a^{2} + \frac{2455664}{49} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 3\) , \( a^{3} + a^{2} - 4 a - 4\) , \( 79 a^{3} + 125 a^{2} - 434 a - 690\) , \( -831 a^{3} - 1336 a^{2} + 4502 a + 7239\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(79a^{3}+125a^{2}-434a-690\right){x}-831a^{3}-1336a^{2}+4502a+7239$ |
*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.
