| 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 |
| 6336.a.152064.1 |
6336.a |
\( 2^{6} \cdot 3^{2} \cdot 11 \) |
\( 2^{9} \cdot 3^{3} \cdot 11 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.027391\) |
\(16.866005\) |
\(0.615972\) |
$[68,1369,33335,-19008]$ |
$[68,-720,-11664,-327888,-152064]$ |
$[-2839714/297,49130/33,7803/22]$ |
$y^2 + (x^3 + x)y = -x^4 - 2x^3 + 2x + 1$ |
| 6336.b.513216.1 |
6336.b |
\( 2^{6} \cdot 3^{2} \cdot 11 \) |
\( 2^{6} \cdot 3^{6} \cdot 11 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.337901\) |
\(9.904564\) |
\(0.836690\) |
$[76528,15349,391422106,64152]$ |
$[76528,244012050,1037343884544,4960993062795183,513216]$ |
$[41013028862818453798912/8019,189867171527709001600/891,106538309182127104/9]$ |
$y^2 + xy = -x^6 + 14x^4 - 65x^2 + 99$ |
| 6336.c.513216.1 |
6336.c |
\( 2^{6} \cdot 3^{2} \cdot 11 \) |
\( - 2^{6} \cdot 3^{6} \cdot 11 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(4.232143\) |
\(1.058036\) |
$[76528,15349,391422106,64152]$ |
$[76528,244012050,1037343884544,4960993062795183,513216]$ |
$[41013028862818453798912/8019,189867171527709001600/891,106538309182127104/9]$ |
$y^2 + xy = -x^6 - 14x^4 - 65x^2 - 99$ |
