| 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 |
| 43264.a.43264.1 |
43264.a |
\( 2^{8} \cdot 13^{2} \) |
\( - 2^{8} \cdot 13^{2} \) |
$0$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.2160.21 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.655431\) |
\(1.478985\) |
$[744,114,13602,5408]$ |
$[744,22988,956928,45876572,43264]$ |
$[890481112704/169,36981117432/169,2069117568/169]$ |
$y^2 + xy = -x^6 - 3x^4 - 3x^2 - 1$ |
| 43264.b.43264.1 |
43264.b |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$2$ |
$2$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.30.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.714729\) |
\(13.132786\) |
\(1.042932\) |
$[744,114,13602,5408]$ |
$[744,22988,956928,45876572,43264]$ |
$[890481112704/169,36981117432/169,2069117568/169]$ |
$y^2 + xy = -x^6 + 3x^4 - 3x^2 + 1$ |
| 43264.c.43264.1 |
43264.c |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1440.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.105046\) |
\(1.444065\) |
$[110,520,15470,169]$ |
$[220,630,-620,-133325,43264]$ |
$[2013137500/169,52408125/338,-468875/676]$ |
$y^2 = x^5 - 5x^3 + 5x^2 - x$ |
| 43264.d.86528.1 |
43264.d |
\( 2^{8} \cdot 13^{2} \) |
\( - 2^{9} \cdot 13^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$6$ |
$0$ |
2.60.2, 3.45.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.033131\) |
\(18.136693\) |
\(1.802660\) |
$[8,181,519,-338]$ |
$[16,-472,-1536,-61840,-86528]$ |
$[-2048/169,3776/169,768/169]$ |
$y^2 + x^3y = x^5 + x^4 + 2x^2 + 4x + 2$ |
| 43264.e.692224.1 |
43264.e |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{12} \cdot 13^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.30.2, 3.720.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(5.066873\) |
\(0.333557\) |
\(1.690093\) |
$[26296,12264082,93182209894,86528]$ |
$[26296,20635596,18983526400,18340746984796,692224]$ |
$[3069647505980681656/169,183212937388525797/338,3204766002294400/169]$ |
$y^2 + xy = -x^6 + 13x^4 - 45x^2 + 16$ |
| 43264.f.692224.1 |
43264.f |
\( 2^{8} \cdot 13^{2} \) |
\( - 2^{12} \cdot 13^{2} \) |
$1$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(0.400341\) |
\(1.667400\) |
\(1.335058\) |
$[26296,12264082,93182209894,86528]$ |
$[26296,20635596,18983526400,18340746984796,692224]$ |
$[3069647505980681656/169,183212937388525797/338,3204766002294400/169]$ |
$y^2 + xy = -x^6 - 13x^4 - 45x^2 - 16$ |
