| 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 |
| 100352.a.100352.1 |
100352.a |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.135.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.501978\) |
\(2.125494\) |
$[56,-80,-404,392]$ |
$[112,736,-512,-149760,100352]$ |
$[175616,10304,-64]$ |
$y^2 = x^5 - x^4 + x^2 + x$ |
| 100352.b.100352.1 |
100352.b |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.120.5, 3.40.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.137847\) |
\(2.034462\) |
$[342,2436,250236,392]$ |
$[684,12998,195556,-8796925,100352]$ |
$[146211169851/98,32496371289/784,1429563249/1568]$ |
$y^2 = x^5 + x^4 - 5x^3 - 2x^2 + 4x - 1$ |
| 100352.c.100352.1 |
100352.c |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.120.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.026921\) |
\(10.319985\) |
\(2.649452\) |
$[1046,1036,356188,392]$ |
$[2092,179590,20265956,2535952963,100352]$ |
$[39129873538843/98,12845683618265/784,1385831669681/1568]$ |
$y^2 = x^5 - 9x^3 + 7x^2 + 14x - 14$ |
| 100352.d.100352.1 |
100352.d |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.120.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.695932\) |
\(11.589322\) |
\(2.016345\) |
$[304,1372,149940,392]$ |
$[608,11744,71936,-23546112,100352]$ |
$[40568406016/49,1288833536/49,12984448/49]$ |
$y^2 = x^5 - x^4 - 4x^3 + 3x^2 + 4x - 2$ |
| 100352.e.100352.1 |
100352.e |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.120.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.697440\) |
\(15.415549\) |
\(2.687856\) |
$[304,1372,149940,392]$ |
$[608,11744,71936,-23546112,100352]$ |
$[40568406016/49,1288833536/49,12984448/49]$ |
$y^2 = x^5 + x^4 - 4x^3 - 3x^2 + 4x + 2$ |
| 100352.f.401408.1 |
100352.f |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.120.5 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.371860\) |
\(6.653457\) |
\(2.474154\) |
$[451,1330,187628,49]$ |
$[1804,121414,10025348,836092099,401408]$ |
$[18658757027251/392,5568886892657/3136,509791452137/6272]$ |
$y^2 = 2x^5 - 6x^4 - 9x^3 + x^2 + 4x + 1$ |
| 100352.g.401408.1 |
100352.g |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.189037\) |
\(10.043568\) |
\(1.898607\) |
$[19,-68,-284,49]$ |
$[76,966,1860,-197949,401408]$ |
$[2476099/392,473271/448,167865/6272]$ |
$y^2 = x^5 + 2x^4 + x^3 - x^2 + 1$ |
