| 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 |
| 36864.a.36864.1 |
36864.a |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathsf{RM}\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.5, 3.36.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.941303\) |
\(1.485326\) |
$[62,-92,-2096,144]$ |
$[124,886,10868,140659,36864]$ |
$[28629151/36,13197413/288,2611037/576]$ |
$y^2 = x^5 - x^4 - x^3 + x^2 + x - 1$ |
| 36864.b.36864.1 |
36864.b |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.675802\) |
\(9.381457\) |
\(1.585002\) |
$[46,-44,-72,144]$ |
$[92,470,-684,-70957,36864]$ |
$[6436343/36,2859245/288,-10051/64]$ |
$y^2 = x^5 - x^3 + x$ |
| 36864.c.36864.1 |
36864.c |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathsf{RM}\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.5, 3.36.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.506281\) |
\(13.551199\) |
\(1.715179\) |
$[62,-92,-2096,144]$ |
$[124,886,10868,140659,36864]$ |
$[28629151/36,13197413/288,2611037/576]$ |
$y^2 = x^5 + x^4 - x^3 - x^2 + x + 1$ |
| 36864.d.221184.1 |
36864.d |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{13} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.832082\) |
\(8.169892\) |
\(1.699505\) |
$[51,36,846,27]$ |
$[204,1350,-6716,-798141,221184]$ |
$[12778713/8,3316275/64,-485231/384]$ |
$y^2 = x^5 - x^4 + 3x^3 - 2x^2 + 2x$ |
| 36864.e.442368.1 |
36864.e |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(11.143802\) |
\(1.392975\) |
$[99,198,6138,54]$ |
$[396,4422,26884,-2227005,442368]$ |
$[352218537/16,79456707/128,2439723/256]$ |
$y^2 = x^5 + 3x^4 - x^3 - 9x^2 - 6x$ |
| 36864.f.442368.1 |
36864.f |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{3} \) |
$1$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.865926\) |
\(15.925274\) |
\(1.723764\) |
$[99,198,6138,54]$ |
$[396,4422,26884,-2227005,442368]$ |
$[352218537/16,79456707/128,2439723/256]$ |
$y^2 = x^5 - 3x^4 - x^3 + 9x^2 - 6x$ |
