| 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 |
| 200704.a.401408.1 |
200704.a |
\( 2^{12} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(4.625319\) |
\(2.312660\) |
$[43,16,-62,49]$ |
$[172,1062,23460,726819,401408]$ |
$[\frac{147008443}{392},\frac{42218217}{3136},\frac{10844385}{6272}]$ |
$y^2 = x^5 - x^3 - x^2 + 2x - 1$ |
| 200704.b.401408.1 |
200704.b |
\( 2^{12} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.120.5 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(6.485390\) |
\(3.242695\) |
$[195,1386,73458,49]$ |
$[780,10566,122756,-3972669,401408]$ |
$[\frac{281950621875}{392},\frac{39172784625}{3136},\frac{1166949225}{6272}]$ |
$y^2 = 2x^5 - 4x^4 - 3x^3 + 4x^2 + x - 1$ |
| 200704.c.401408.1 |
200704.c |
\( 2^{12} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.235677\) |
\(5.296335\) |
\(3.272279\) |
$[19,-68,-284,49]$ |
$[76,966,1860,-197949,401408]$ |
$[\frac{2476099}{392},\frac{473271}{448},\frac{167865}{6272}]$ |
$y^2 = x^5 - 2x^4 + x^3 + x^2 - 1$ |
| 200704.d.401408.1 |
200704.d |
\( 2^{12} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.120.5 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.336432\) |
\(16.214168\) |
\(2.727484\) |
$[451,1330,187628,49]$ |
$[1804,121414,10025348,836092099,401408]$ |
$[\frac{18658757027251}{392},\frac{5568886892657}{3136},\frac{509791452137}{6272}]$ |
$y^2 = 2x^5 + 6x^4 - 9x^3 - x^2 + 4x - 1$ |
