| 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 |
| 110976.a.110976.1 |
110976.a |
\( 2^{7} \cdot 3 \cdot 17^{2} \) |
\( - 2^{7} \cdot 3 \cdot 17^{2} \) |
$2$ |
$4$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.5, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(0.633344\) |
\(5.363378\) |
\(1.698431\) |
$[4944,7005,11407566,13872]$ |
$[4944,1013794,276011520,84205670111,110976]$ |
$[\frac{7692386305499136}{289},\frac{319046421956544}{289},\frac{17569237294080}{289}]$ |
$y^2 + xy = -x^6 - 6x^4 - 11x^2 - 6$ |
| 110976.b.110976.1 |
110976.b |
\( 2^{7} \cdot 3 \cdot 17^{2} \) |
\( 2^{7} \cdot 3 \cdot 17^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.5, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.410019\) |
\(16.027499\) |
\(1.642896\) |
$[4944,7005,11407566,13872]$ |
$[4944,1013794,276011520,84205670111,110976]$ |
$[\frac{7692386305499136}{289},\frac{319046421956544}{289},\frac{17569237294080}{289}]$ |
$y^2 + xy = -x^6 + 6x^4 - 11x^2 + 6$ |
| 110976.c.332928.1 |
110976.c |
\( 2^{7} \cdot 3 \cdot 17^{2} \) |
\( - 2^{7} \cdot 3^{2} \cdot 17^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.077507\) |
\(10.835649\) |
\(1.679675\) |
$[248,1207,83147,41616]$ |
$[248,1758,16832,270943,332928]$ |
$[\frac{7329062656}{2601},\frac{69830104}{867},\frac{8087776}{2601}]$ |
$y^2 + (x^3 + x^2)y = 2x^4 + 4x^3 + 5x^2 + 4x + 2$ |
| 110976.d.887808.1 |
110976.d |
\( 2^{7} \cdot 3 \cdot 17^{2} \) |
\( 2^{10} \cdot 3 \cdot 17^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$10$ |
$0$ |
2.45.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.122472\) |
\(11.610814\) |
\(1.422000\) |
$[2600,5272,4559044,110976]$ |
$[2600,278152,39171072,6119063024,887808]$ |
$[\frac{116029062500000}{867},\frac{4774218312500}{867},\frac{86196760000}{289}]$ |
$y^2 + xy = x^6 - 5x^4 + 7x^2 - 3$ |
| 110976.e.887808.1 |
110976.e |
\( 2^{7} \cdot 3 \cdot 17^{2} \) |
\( - 2^{10} \cdot 3 \cdot 17^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.286508\) |
\(6.497500\) |
\(1.861584\) |
$[2600,5272,4559044,110976]$ |
$[2600,278152,39171072,6119063024,887808]$ |
$[\frac{116029062500000}{867},\frac{4774218312500}{867},\frac{86196760000}{289}]$ |
$y^2 + xy = x^6 + 5x^4 + 7x^2 + 3$ |
