| 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 |
| 13248.a.13248.1 |
13248.a |
\( 2^{6} \cdot 3^{2} \cdot 23 \) |
\( 2^{6} \cdot 3^{2} \cdot 23 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.45.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.454195\) |
\(9.458560\) |
\(1.074007\) |
$[188,412,33544,1656]$ |
$[188,1198,-92,-363125,13248]$ |
$[3669520112/207,124379954/207,-2209/9]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 + x^3 - 2x^2 + x - 1$ |
| 13248.b.13248.1 |
13248.b |
\( 2^{6} \cdot 3^{2} \cdot 23 \) |
\( 2^{6} \cdot 3^{2} \cdot 23 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.709473\) |
\(4.463164\) |
\(0.791623\) |
$[2884,146671,159743442,1656]$ |
$[2884,248780,-8134272,-21337682212,13248]$ |
$[3117427098681616/207,93244077709580/207,-5106917984]$ |
$y^2 + (x^3 + x)y = -8x^2 - 23$ |
| 13248.c.13248.1 |
13248.c |
\( 2^{6} \cdot 3^{2} \cdot 23 \) |
\( - 2^{6} \cdot 3^{2} \cdot 23 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.177368\) |
\(20.890451\) |
\(0.926325\) |
$[2884,146671,159743442,1656]$ |
$[2884,248780,-8134272,-21337682212,13248]$ |
$[3117427098681616/207,93244077709580/207,-5106917984]$ |
$y^2 + (x^3 + x)y = -x^4 - 8x^2 + 23$ |
