| 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 |
| 961.a.961.1 |
961.a |
\( 31^{2} \) |
\( - 31^{2} \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.2, 3.72.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.224644\) |
\(0.449288\) |
$[66980,1011437281,14016353908561,-123008]$ |
$[16745,-30460094,12221475912,-180792178085599,-961]$ |
$[-1316514841399349215625/961,143016680917998700750/961,-3426841043882137800/961]$ |
$y^2 + (x^3 + x + 1)y = -x^6 - x^5 - 7x^4 + 74x^3 - 145x^2 + 99x - 33$ |
| 961.a.961.2 |
961.a |
\( 31^{2} \) |
\( - 31^{2} \) |
$0$ |
$1$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.2, 3.72.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(5.616097\) |
\(0.449288\) |
$[11260,503521,1770579599,123008]$ |
$[2815,309196,43449708,6677190401,961]$ |
$[176763257309509375/961,6897140364776500/961,344305262376300/961]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7$ |
| 961.a.961.3 |
961.a |
\( 31^{2} \) |
\( 31^{2} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.120.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.232193\) |
\(0.449288\) |
$[260,1681,185209,123008]$ |
$[65,106,-672,-13729,961]$ |
$[1160290625/961,29110250/961,-2839200/961]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1$ |
| 961.a.923521.1 |
961.a |
\( 31^{2} \) |
\( 31^{4} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.120.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(2.246439\) |
\(0.449288\) |
$[4100,78961,94151689,118210688]$ |
$[1025,40486,2121888,133954751,923521]$ |
$[1131408212890625/923521,1406419156250/29791,2319780000/961]$ |
$y^2 + (x^3 + x^2 + 1)y = -5x^4 + 4x^3 + 3x^2 - 2x - 3$ |
