| 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 |
| 11664.a.11664.1 |
11664.a |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{6} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\Q \times \Q\) |
✓ |
$D_{6,2}$ |
|
|
|
$C_2^2$ |
$C_3:D_4$ |
$2$ |
$0$ |
2.120.2, 3.8640.7 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.900641\) |
\(10.216231\) |
\(1.022351\) |
$[40,45,555,6]$ |
$[120,330,-320,-36825,11664]$ |
$[6400000/3,440000/9,-32000/81]$ |
$y^2 + y = -x^6$ |
| 11664.b.34992.1 |
11664.b |
\( 2^{4} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{7} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.120.4, 3.2160.20 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(6.686669\) |
\(0.742963\) |
$[216,45,2709,18]$ |
$[648,17226,613440,25193511,34992]$ |
$[3265173504,133949376,7361280]$ |
$y^2 + y = -x^6 - 3x^4 - 3x^2 - 1$ |
| 11664.b.944784.1 |
11664.b |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{10} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.120.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(6.686669\) |
\(0.742963\) |
$[248,6165,349593,-486]$ |
$[744,-13926,207680,-9854889,-944784]$ |
$[-58632501248/243,4425274304/729,-798321920/6561]$ |
$y^2 + x^3y = 3x^4 + 9x^2 - 1$ |
| 11664.c.34992.1 |
11664.c |
\( 2^{4} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{7} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(14.025272\) |
\(0.779182\) |
$[80,-792,-20508,-576]$ |
$[120,1788,25924,-21516,-34992]$ |
$[-6400000/9,-2384000/27,-2592400/243]$ |
$y^2 + (x + 1)y = -x^6 + 2x^2 + x$ |
| 11664.d.139968.1 |
11664.d |
\( 2^{4} \cdot 3^{6} \) |
\( - 2^{6} \cdot 3^{7} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.020176\) |
\(19.103818\) |
\(0.963582\) |
$[48,288,1848,-72]$ |
$[144,-864,31680,953856,-139968]$ |
$[-442368,18432,-14080/3]$ |
$y^2 + y = 2x^5 + 3x^4 - 2x^3 - x^2$ |
| 11664.e.314928.1 |
11664.e |
\( 2^{4} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{9} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.213511\) |
\(7.338972\) |
\(0.783475\) |
$[24,-72,-7236,-5184]$ |
$[36,162,20736,180063,-314928]$ |
$[-192,-24,-256/3]$ |
$y^2 + x^2y = x^5 - 5x^3 - 7x^2 - 4x - 1$ |
| 11664.f.559872.1 |
11664.f |
\( 2^{4} \cdot 3^{6} \) |
\( - 2^{8} \cdot 3^{7} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.042219\) |
\(14.721058\) |
\(0.621505\) |
$[2,96,-3043,-9]$ |
$[12,-2298,591940,455619,-559872]$ |
$[-4/9,383/54,-147985/972]$ |
$y^2 + y = 4x^5 - 5x^4 + x^3 + 4x^2 - 2x$ |
