| 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 |
| 100096.a.100096.1 |
100096.a |
\( 2^{8} \cdot 17 \cdot 23 \) |
\( - 2^{8} \cdot 17 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(3.616386\) |
\(0.904096\) |
$[450,2088,442170,391]$ |
$[900,28182,-64820,-213140781,100096]$ |
$[2306601562500/391,160505296875/782,-820378125/1564]$ |
$y^2 = x^5 - 2x^4 - 3x^3 - 7x^2 - 7x - 2$ |
| 100096.b.100096.1 |
100096.b |
\( 2^{8} \cdot 17 \cdot 23 \) |
\( - 2^{8} \cdot 17 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(6.972917\) |
\(1.743229\) |
$[1326,-1344,-597342,-391]$ |
$[2652,296630,44782996,7693787123,-100096]$ |
$[-30142461298716/23,-2542592373165/46,-289488481893/92]$ |
$y^2 = x^5 - 9x^3 + 5x^2 + 21x - 20$ |
| 100096.c.100096.1 |
100096.c |
\( 2^{8} \cdot 17 \cdot 23 \) |
\( - 2^{8} \cdot 17 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.273964\) |
\(2.818491\) |
$[1326,-1344,-597342,-391]$ |
$[2652,296630,44782996,7693787123,-100096]$ |
$[-30142461298716/23,-2542592373165/46,-289488481893/92]$ |
$y^2 = x^5 - 9x^3 - 5x^2 + 21x + 20$ |
