| 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 |
| 5769.a.17307.1 |
5769.a |
\( 3^{2} \cdot 641 \) |
\( - 3^{3} \cdot 641 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.083425\) |
\(12.708566\) |
\(0.530105\) |
$[240,-1764,-139905,-69228]$ |
$[120,894,9745,92541,-17307]$ |
$[-921600000/641,-57216000/641,-15592000/1923]$ |
$y^2 + (x^2 + 1)y = x^5 - 2x^4 - x^3 + x$ |
| 5769.b.17307.1 |
5769.b |
\( 3^{2} \cdot 641 \) |
\( - 3^{3} \cdot 641 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.005378\) |
\(24.769580\) |
\(0.266444\) |
$[324,19881,1386405,-2215296]$ |
$[81,-555,613,-64593,-17307]$ |
$[-129140163/641,10924065/641,-148959/641]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 3x^3$ |
| 5769.c.17307.1 |
5769.c |
\( 3^{2} \cdot 641 \) |
\( - 3^{3} \cdot 641 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.829725\) |
\(0.713429\) |
$[536,6808,1509445,69228]$ |
$[268,1858,-38689,-3455204,17307]$ |
$[1382528109568/17307,35764329856/17307,-2778798736/17307]$ |
$y^2 + (x^3 + x^2)y = -x^4 - x^3 - x + 2$ |
