| 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 |
| 331776.a.663552.1 |
331776.a |
\( 2^{12} \cdot 3^{4} \) |
\( 2^{13} \cdot 3^{4} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.120.5 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.985001\) |
\(5.876114\) |
\(2.893988\) |
$[1443,2106,984474,81]$ |
$[5772,1365702,425150212,147206267715,663552]$ |
$[\frac{77240777479203}{8},\frac{25330276130497}{64},\frac{24590794549633}{1152}]$ |
$y^2 = -x^6 - 4x^5 + 11x^3 - 9x + 3$ |
| 331776.b.663552.1 |
331776.b |
\( 2^{12} \cdot 3^{4} \) |
\( 2^{13} \cdot 3^{4} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.40.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.577418\) |
\(7.585408\) |
\(2.189976\) |
$[189,2664,121788,-81]$ |
$[756,-4602,39164,2107395,-663552]$ |
$[-\frac{2977309629}{8},\frac{191786049}{64},-\frac{4317831}{128}]$ |
$y^2 = x^5 + 2x^4 - 5x^3 + 9x^2 - 6x + 3$ |
| 331776.c.663552.1 |
331776.c |
\( 2^{12} \cdot 3^{4} \) |
\( 2^{13} \cdot 3^{4} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.120.5 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.489946\) |
\(2.744973\) |
$[243,2682,171432,81]$ |
$[972,10758,97348,-5278077,663552]$ |
$[\frac{10460353203}{8},\frac{952873713}{64},\frac{17741673}{128}]$ |
$y^2 = 2x^5 - 6x^4 - x^3 + 5x^2 - 1$ |
| 331776.d.995328.1 |
331776.d |
\( 2^{12} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{5} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathsf{RM}\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.90.3, 3.36.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(2.976000\) |
\(1.488000\) |
$[106,-20,-1232,16]$ |
$[636,17334,747252,43696179,995328]$ |
$[\frac{418195493}{4},\frac{143368551}{32},\frac{19435471}{64}]$ |
$y^2 = x^5 + x^4 + x^3 - 7x^2 + 5x - 1$ |
| 331776.e.995328.1 |
331776.e |
\( 2^{12} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{5} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.90.3, 3.540.7 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(6.346552\) |
\(3.173276\) |
$[58,28,856,16]$ |
$[348,4374,-1836,-4942701,995328]$ |
$[\frac{20511149}{4},\frac{5926527}{32},-\frac{14297}{64}]$ |
$y^2 = x^5 + 3x^3 + 3x$ |
| 331776.f.995328.1 |
331776.f |
\( 2^{12} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{5} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathsf{RM}\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3, 3.36.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.556679\) |
\(12.163955\) |
\(3.385708\) |
$[106,-20,-1232,16]$ |
$[636,17334,747252,43696179,995328]$ |
$[\frac{418195493}{4},\frac{143368551}{32},\frac{19435471}{64}]$ |
$y^2 = x^5 - x^4 + x^3 + 7x^2 + 5x + 1$ |
| 331776.g.995328.1 |
331776.g |
\( 2^{12} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{5} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$2$ |
2.90.3, 3.540.7 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.770890\) |
\(6.346552\) |
\(2.446248\) |
$[58,28,856,16]$ |
$[348,4374,-1836,-4942701,995328]$ |
$[\frac{20511149}{4},\frac{5926527}{32},-\frac{14297}{64}]$ |
$y^2 = x^5 - 3x^3 + 3x$ |
