| 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 |
| 6400.a.12800.1 |
6400.a |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{9} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1, 3.120.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.116427\) |
\(12.485972\) |
\(0.726850\) |
$[6,150,1200,50]$ |
$[12,-394,-7196,-60397,12800]$ |
$[486/25,-5319/100,-16191/200]$ |
$y^2 + y = 2x^5 - 3x^4 + 3x^3 - x^2$ |
| 6400.b.12800.1 |
6400.b |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$0$ |
2.180.4, 3.8640.8 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(11.281316\) |
\(0.940110\) |
$[248,181,14873,50]$ |
$[496,9768,243200,6303344,12800]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 + x^3y = 2x^4 + 4x^2 + 2$ |
| 6400.c.12800.1 |
6400.c |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{9} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(8.064054\) |
\(0.672005\) |
$[120,309,14889,50]$ |
$[240,1576,-18944,-1757584,12800]$ |
$[62208000,1702080,-85248]$ |
$y^2 + x^3y = -2x^2 - 2$ |
| 6400.d.12800.1 |
6400.d |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{9} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$6$ |
$0$ |
2.180.4, 3.8640.8 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.413437\) |
\(18.167258\) |
\(0.625918\) |
$[248,181,14873,50]$ |
$[496,9768,243200,6303344,12800]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 + x^3y = -2x^4 + 4x^2 - 2$ |
| 6400.e.12800.1 |
6400.e |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.45.1, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.361103\) |
\(23.716575\) |
\(0.713677\) |
$[120,309,14889,50]$ |
$[240,1576,-18944,-1757584,12800]$ |
$[62208000,1702080,-85248]$ |
$y^2 + x^3y = -2x^2 + 2$ |
| 6400.f.64000.1 |
6400.f |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{3} \) |
$2$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$16$ |
$0$ |
2.90.6, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.067032\) |
\(19.455210\) |
\(0.326031\) |
$[154,310,19480,250]$ |
$[308,3126,-164,-2455597,64000]$ |
$[5413568314/125,713561079/500,-243089/1000]$ |
$y^2 + x^3y = -2x^4 - 3x^3 + x^2 + 6x + 4$ |
| 6400.g.64000.1 |
6400.g |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.303153\) |
\(1.575788\) |
$[154,310,19480,250]$ |
$[308,3126,-164,-2455597,64000]$ |
$[5413568314/125,713561079/500,-243089/1000]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^3 - x - 1$ |
| 6400.h.409600.1 |
6400.h |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.1080.9 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(4.591325\) |
\(1.147831\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = -x^6 + 2x^2 - 1$ |
| 6400.i.409600.1 |
6400.i |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$0$ |
$0$ |
2.180.4, 3.8640.12 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.171827\) |
\(1.292957\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = -x^6 - 4x^4 - 4x^2 - 1$ |
| 6400.j.819200.1 |
6400.j |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.45.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.717386\) |
\(16.185160\) |
\(0.725688\) |
$[216,1749,151749,100]$ |
$[864,12448,-2662400,-613816576,819200]$ |
$[14693280768/25,245013984/25,-2426112]$ |
$y^2 = x^6 - 3x^4 + x^2 + 2$ |
| 6400.k.819200.1 |
6400.k |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{15} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(4.470386\) |
\(1.117597\) |
$[216,1749,151749,100]$ |
$[864,12448,-2662400,-613816576,819200]$ |
$[14693280768/25,245013984/25,-2426112]$ |
$y^2 = -x^6 - 3x^4 - x^2 + 2$ |
