| 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 |
| 6272.a.50176.1 |
6272.a |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.90.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.348369\) |
\(14.703120\) |
\(0.569124\) |
$[792,120,15228,6272]$ |
$[792,26056,1154048,58772720,50176]$ |
$[\frac{304316815968}{49},\frac{12641055372}{49},14427072]$ |
$y^2 + xy = x^6 - 3x^4 + 3x^2 - 1$ |
| 6272.b.50176.1 |
6272.b |
\( 2^{7} \cdot 7^{2} \) |
\( - 2^{10} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.534554\) |
\(9.651117\) |
\(0.573227\) |
$[792,120,15228,6272]$ |
$[792,26056,1154048,58772720,50176]$ |
$[\frac{304316815968}{49},\frac{12641055372}{49},14427072]$ |
$y^2 + xy = x^6 + 3x^4 + 3x^2 + 1$ |
| 6272.c.401408.1 |
6272.c |
\( 2^{7} \cdot 7^{2} \) |
\( - 2^{13} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.45.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.479840\) |
\(11.800148\) |
\(0.707773\) |
$[120,408,14988,1568]$ |
$[240,1312,-2048,-553216,401408]$ |
$[\frac{97200000}{49},\frac{2214000}{49},-\frac{14400}{49}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = 2x^4 + 2x^2$ |
