| 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 |
| 32400.a.32400.1 |
32400.a |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.12.1, 3.40.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.060083\) |
\(19.656185\) |
\(1.181008\) |
$[624,9180,1862460,-129600]$ |
$[312,2526,-4036,-1909977,-32400]$ |
$[-2281224192/25,-59195968/25,2728336/225]$ |
$y^2 + (x^3 + x^2)y = -x^2 - 2x + 2$ |
| 32400.b.291600.1 |
32400.b |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.40.1, 3.40.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.129557\) |
\(4.083377\) |
\(1.587085\) |
$[408,17685,1608615,-36450]$ |
$[408,-4854,63536,590343,-291600]$ |
$[-2907867136/75,254375488/225,-73447616/2025]$ |
$y^2 + y = -x^6 - 2x^5 + 2x^4 - 2x^3 - x^2 + x - 1$ |
| 32400.c.388800.1 |
32400.c |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{5} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.123715\) |
\(18.786559\) |
\(1.452616\) |
$[160,2416,87432,-200]$ |
$[480,-4896,90432,4859136,-388800]$ |
$[-65536000,1392640,-160768/3]$ |
$y^2 + y = 2x^5 + 9x^4 + 4x^3 - x^2$ |
| 32400.d.486000.1 |
32400.d |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{5} \cdot 5^{3} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.161599\) |
\(11.365541\) |
\(1.836656\) |
$[12592,1900,7833900,-8000]$ |
$[18888,14862006,15589640196,18394475419503,-486000]$ |
$[-618306218132903936/125,-25757819662387264/125,-4291439937136144/375]$ |
$y^2 + x^2y = 15x^5 + 11x^4 - 12x^3 - x^2 + 14x + 6$ |
| 32400.e.486000.1 |
32400.e |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{5} \cdot 5^{3} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3, 3.2160.24 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(2.342977\) |
\(2.342977\) |
$[3096,252900,172934100,-1944000]$ |
$[1548,57696,7496356,2068882668,-486000]$ |
$[-2286275305536/125,-55046830464/125,-13860762244/375]$ |
$y^2 + x^2y = x^5 - 6x^4 + 7x^3 + 12x - 21$ |
