| Label |
Class |
Equation |
Sato-Tate |
\(\overline{\Q}\)-simple |
\(\GL_2\) |
Rank* |
| 256.a.512.1 |
256.a |
\(y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x\) |
$E_4$ |
|
✓ |
0 |
| 324.a.648.1 |
324.a |
\(y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2\) |
$E_3$ |
|
✓ |
0 |
| 388.a.776.1 |
388.a |
\(y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 472.a.944.1 |
472.a |
\(y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 476.a.952.1 |
476.a |
\(y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54\) |
$G_{3,3}$ |
|
✓ |
0 |
| 523.a.523.1 |
523.a |
\(y^2 + (x + 1)y = x^5 - x^4 - x^3\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 523.a.523.2 |
523.a |
\(y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 529.a.529.1 |
529.a |
\(y^2 + (x^3 + x + 1)y = -x^5\) |
$G_{3,3}$ |
✓ |
✓ |
0 |
| 576.a.576.1 |
576.a |
\(y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x\) |
$E_2$ |
|
✓ |
0 |
| 587.a.587.1 |
587.a |
\(y^2 + (x^3 + x + 1)y = -x^2 - x\) |
$\mathrm{USp}(4)$ |
✓ |
|
1 |
| 597.a.597.1 |
597.a |
\(y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 603.a.603.1 |
603.a |
\(y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 603.a.603.2 |
603.a |
\(y^2 + (x^2 + 1)y = x^5 - x^3 + x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 686.a.686.1 |
686.a |
\(y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x\) |
$N(G_{1,3})$ |
|
✓ |
0 |
| 691.a.691.1 |
691.a |
\(y^2 + (x + 1)y = x^5 - x^3 - x^2\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 709.a.709.1 |
709.a |
\(y^2 + xy = x^5 - 2x^2 + x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 713.a.713.1 |
713.a |
\(y^2 + (x^3 + x + 1)y = -x^5 - x\) |
$\mathrm{USp}(4)$ |
✓ |
|
1 |
| 713.b.713.1 |
713.b |
\(y^2 + (x^3 + x + 1)y = -x^4\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 743.a.743.1 |
743.a |
\(y^2 + (x^3 + x + 1)y = -x^4 + x^2\) |
$\mathrm{USp}(4)$ |
✓ |
|
1 |
| 745.a.745.1 |
745.a |
\(y^2 + (x^3 + x + 1)y = -x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 763.a.763.1 |
763.a |
\(y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 797.a.797.1 |
797.a |
\(y^2 + y = x^5 - x^4 + x^3\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 832.a.832.1 |
832.a |
\(y^2 + (x^3 + x)y = x^5 - x^3 + x^2 + 2x - 1\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 841.a.841.1 |
841.a |
\(y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2\) |
$G_{3,3}$ |
✓ |
✓ |
0 |
| 847.a.847.1 |
847.a |
\(y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2\) |
$G_{3,3}$ |
|
✓ |
1 |
| 847.d.847.1 |
847.d |
\(y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12\) |
$G_{3,3}$ |
|
✓ |
0 |
| 862.a.862.1 |
862.a |
\(y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 862.b.862.1 |
862.b |
\(y^2 + (x^3 + x)y = -2x^4 + 3x^2 - x - 1\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 893.a.893.1 |
893.a |
\(y^2 + (x^3 + x + 1)y = -x^4 - x^2\) |
$\mathrm{USp}(4)$ |
✓ |
|
1 |
| 909.a.909.1 |
909.a |
\(y^2 + (x^3 + x)y = -x^4 + x^2 - x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 925.a.925.1 |
925.a |
\(y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 930.a.930.1 |
930.a |
\(y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15\) |
$G_{3,3}$ |
|
✓ |
0 |
| 953.a.953.1 |
953.a |
\(y^2 + (x^3 + x + 1)y = x^3 + x^2\) |
$\mathrm{USp}(4)$ |
✓ |
|
1 |
| 961.a.961.1 |
961.a |
\(y^2 + (x^3 + x + 1)y = -x^6 - x^5 - 7x^4 + 74x^3 - 145x^2 + 99x - 33\) |
$G_{3,3}$ |
✓ |
✓ |
0 |
| 961.a.961.2 |
961.a |
\(y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7\) |
$G_{3,3}$ |
✓ |
✓ |
0 |
| 961.a.961.3 |
961.a |
\(y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1\) |
$G_{3,3}$ |
✓ |
✓ |
0 |
| 971.a.971.1 |
971.a |
\(y^2 + y = x^5 - 2x^3 + x\) |
$\mathrm{USp}(4)$ |
✓ |
|
1 |
| 997.a.997.1 |
997.a |
\(y^2 + xy = x^5 - 8x^4 + 16x^3 - x\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 997.a.997.2 |
997.a |
\(y^2 + (x + 1)y = x^5 + x^4\) |
$\mathrm{USp}(4)$ |
✓ |
|
0 |
| 997.b.997.1 |
997.b |
\(y^2 + y = x^5 - 2x^4 + 2x^3 - x^2\) |
$\mathrm{USp}(4)$ |
✓ |
|
1 |
