| 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 |
| 1077.a.1077.2 |
1077.a |
\( 3 \cdot 359 \) |
\( - 3 \cdot 359 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.035633\) |
\(21.235034\) |
\(0.189165\) |
$[268,2233,175667,137856]$ |
$[67,94,-12,-2410,1077]$ |
$[1350125107/1077,28271722/1077,-17956/359]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 + 2x^2 + x$ |
| 1077.a.1077.1 |
1077.a |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.035633\) |
\(21.235034\) |
\(0.189165\) |
$[155924,161593,8379938029,137856]$ |
$[38981,63306532,137068427976,333836849266358,1077]$ |
$[90004636142290020118901/1077,3749794358746968581012/1077,69425997674312689112/359]$ |
$y^2 + (x^3 + 1)y = 5x^5 + 34x^4 + 80x^3 - x^2 - 90x + 32$ |
| 1077.b.1077.1 |
1077.b |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.157286\) |
\(0.406291\) |
$[320,544,55360,4308]$ |
$[160,976,7360,56256,1077]$ |
$[104857600000/1077,3997696000/1077,188416000/1077]$ |
$y^2 + x^3y = x^5 + x^4 - x - 2$ |
| 1077.b.1077.2 |
1077.b |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.406291\) |
\(0.406291\) |
$[107840,22281904,765878465200,4308]$ |
$[53920,117426616,333407026000,1047074174177136,1077]$ |
$[455773864377135923200000/1077,18408406506675601408000/1077,969336384916326400000/1077]$ |
$y^2 + y = x^5 + 14x^4 + 38x^3 - 79x^2 + 15x - 1$ |
