| 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 |
| 65280.a.130560.1 |
65280.a |
\( 2^{8} \cdot 3 \cdot 5 \cdot 17 \) |
\( 2^{9} \cdot 3 \cdot 5 \cdot 17 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.039573\) |
\(15.705793\) |
\(1.243054\) |
$[100,394,3248,16320]$ |
$[100,154,6724,162171,130560]$ |
$[3906250/51,240625/204,210125/408]$ |
$y^2 + (x + 1)y = x^6 + 4x^5 + 6x^4 + 3x^3$ |
| 65280.b.130560.1 |
65280.b |
\( 2^{8} \cdot 3 \cdot 5 \cdot 17 \) |
\( - 2^{9} \cdot 3 \cdot 5 \cdot 17 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(8.915507\) |
\(4.457754\) |
$[470,10,82864,-510]$ |
$[940,36790,1340356,-23392365,-130560]$ |
$[-286681258750/51,-47745602125/204,-3701058005/408]$ |
$y^2 + y = 2x^5 - x^4 - 5x^3 + 4x + 1$ |
| 65280.c.130560.1 |
65280.c |
\( 2^{8} \cdot 3 \cdot 5 \cdot 17 \) |
\( 2^{9} \cdot 3 \cdot 5 \cdot 17 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.90.6 |
✓ |
✓ |
$4$ |
\( 2 \) |
\(1.000000\) |
\(5.677386\) |
\(2.838693\) |
$[12006,9714,38598408,510]$ |
$[24012,23998102,31946326116,47796570773747,130560]$ |
$[5196972966481620162/85,865228217564745459/340,95934841286092587/680]$ |
$y^2 + x^3y = x^6 - 3x^5 - 9x^4 + 13x^3 + 23x^2 - 14x - 20$ |
| 65280.d.130560.1 |
65280.d |
\( 2^{8} \cdot 3 \cdot 5 \cdot 17 \) |
\( 2^{9} \cdot 3 \cdot 5 \cdot 17 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.90.6 |
✓ |
✓ |
$4$ |
\( 2 \) |
\(1.000000\) |
\(8.340060\) |
\(4.170030\) |
$[12326,6514,26902008,510]$ |
$[24652,25304342,34607139556,53206370070387,130560]$ |
$[17782418802672894086/255,2961703347198983737/1020,328617016519599841/2040]$ |
$y^2 + y = 20x^6 - 38x^5 + x^4 + 21x^3 - 4x - 1$ |
| 65280.e.130560.1 |
65280.e |
\( 2^{8} \cdot 3 \cdot 5 \cdot 17 \) |
\( 2^{9} \cdot 3 \cdot 5 \cdot 17 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.90.6 |
✓ |
✓ |
$36$ |
\( 2 \) |
\(1.000000\) |
\(0.917392\) |
\(4.128265\) |
$[14918,13717618,51277691208,510]$ |
$[29836,510806,8752420,53608371,130560]$ |
$[46177777988075362598/255,105990713496087337/1020,24347779975901/408]$ |
$y^2 + y = -28x^6 - 86x^5 - 57x^4 + 45x^3 + 49x^2 - x - 7$ |
| 65280.f.261120.1 |
65280.f |
\( 2^{8} \cdot 3 \cdot 5 \cdot 17 \) |
\( - 2^{10} \cdot 3 \cdot 5 \cdot 17 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.40.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.454108\) |
\(1.363527\) |
$[10,-3032,14436,1020]$ |
$[20,8102,-147556,-17148381,261120]$ |
$[625/51,101275/408,-184445/816]$ |
$y^2 = x^5 + 2x^4 + x^3 + 3x^2 + 2x - 3$ |
