| Label |
Class |
Conductor |
Discriminant |
Rank* |
2-Selmer rank |
Torsion |
$\textrm{End}^0(J_{\overline\Q})$ |
$\textrm{End}^0(J)$ |
$\GL_2\textsf{-type}$ |
Sato-Tate |
Nonmaximal primes |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
mod-$\ell$ images |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 349.a.349.1 |
349.a |
\( 349 \) |
\( 349 \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(27.988484\) |
\(0.165612\) |
$[8,208,1464,-1396]$ |
$[4,-34,-124,-413,-349]$ |
$[-\frac{1024}{349},\frac{2176}{349},\frac{1984}{349}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2$ |
| 2512.a.160768.1 |
2512.a |
\( 2^{4} \cdot 157 \) |
\( - 2^{10} \cdot 157 \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 13 \) |
\(1.000000\) |
\(10.601477\) |
\(0.815498\) |
$[324,1413,145089,20096]$ |
$[324,3432,34544,-146592,160768]$ |
$[\frac{3486784401}{157},\frac{227988189}{314},\frac{14165199}{628}]$ |
$y^2 + (x + 1)y = x^6 + 3x^4 + x^3 + 2x^2$ |
| 4624.d.295936.1 |
4624.d |
\( 2^{4} \cdot 17^{2} \) |
\( 2^{10} \cdot 17^{2} \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.12.1 |
✓ |
✓ |
$1$ |
\( 13 \) |
\(1.000000\) |
\(12.766189\) |
\(0.982015\) |
$[88,-1292,-144636,1183744]$ |
$[44,296,13636,128092,295936]$ |
$[\frac{161051}{289},\frac{49247}{578},\frac{412489}{4624}]$ |
$y^2 + (x^3 + x^2)y = x^3 + x^2 - 2x - 1$ |
| 5200.b.332800.1 |
5200.b |
\( 2^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{10} \cdot 5^{2} \cdot 13 \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 13 \) |
\(1.000000\) |
\(13.486416\) |
\(1.037417\) |
$[8,316,-10722,41600]$ |
$[8,-208,10000,9184,332800]$ |
$[\frac{32}{325},-\frac{8}{25},\frac{25}{13}]$ |
$y^2 + (x + 1)y = x^6 + 2x^5 + 2x^4 - x^2$ |
| 5968.a.381952.1 |
5968.a |
\( 2^{4} \cdot 373 \) |
\( 2^{10} \cdot 373 \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 13 \) |
\(1.000000\) |
\(14.248579\) |
\(1.096045\) |
$[40,1420,18930,-47744]$ |
$[40,-880,-6160,-255200,-381952]$ |
$[-\frac{100000}{373},\frac{55000}{373},\frac{9625}{373}]$ |
$y^2 + (x + 1)y = x^6 + 2x^5 + x^2$ |
| 6544.b.418816.1 |
6544.b |
\( 2^{4} \cdot 409 \) |
\( 2^{10} \cdot 409 \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 13 \) |
\(1.000000\) |
\(14.196880\) |
\(1.092068\) |
$[152,9748,354156,-1675264]$ |
$[76,-1384,-4036,-555548,-418816]$ |
$[-\frac{2476099}{409},\frac{1186607}{818},\frac{364249}{6544}]$ |
$y^2 + (x^3 + x)y = x^5 + 2x^2 + x + 1$ |
| 6928.c.443392.1 |
6928.c |
\( 2^{4} \cdot 433 \) |
\( - 2^{10} \cdot 433 \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 13 \) |
\(1.000000\) |
\(16.670347\) |
\(1.282334\) |
$[804,10701,3153213,55424]$ |
$[804,19800,-6544,-99325344,443392]$ |
$[\frac{328080401001}{433},\frac{20098487475}{866},-\frac{16524009}{1732}]$ |
$y^2 + (x + 1)y = x^6 - 4x^5 + 3x^4 + x^3 + 2x^2 + x$ |
