| 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 |
| 18080.a.180800.1 |
18080.a |
\( 2^{5} \cdot 5 \cdot 113 \) |
\( - 2^{6} \cdot 5^{2} \cdot 113 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.119309\) |
\(12.821745\) |
\(1.529745\) |
$[352,10411,876764,22600]$ |
$[352,-1778,256,-767793,180800]$ |
$[84437106688/2825,-1211657216/2825,495616/2825]$ |
$y^2 + xy = x^6 - 2x^4 - 2x^3 + x^2 + 2x + 1$ |
| 18080.b.180800.1 |
18080.b |
\( 2^{5} \cdot 5 \cdot 113 \) |
\( - 2^{6} \cdot 5^{2} \cdot 113 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.061052\) |
\(15.528132\) |
\(0.948017\) |
$[208,2563,152516,22600]$ |
$[208,94,-16016,-835041,180800]$ |
$[6083264512/2825,13217152/2825,-10826816/2825]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 + x^2 - x + 2$ |
| 18080.c.723200.1 |
18080.c |
\( 2^{5} \cdot 5 \cdot 113 \) |
\( - 2^{8} \cdot 5^{2} \cdot 113 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
2.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.022197\) |
\(14.767439\) |
\(0.655575\) |
$[148,2917,148783,90400]$ |
$[148,-1032,-44800,-1923856,723200]$ |
$[277375828/2825,-13068474/2825,-153328/113]$ |
$y^2 + xy = x^6 - 2x^5 + x^3 + x^2 - 2x + 1$ |
