| 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 |
| 114240.a.114240.1 |
114240.a |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
\( - 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
$1$ |
$5$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.5, 3.90.1 |
|
|
$32$ |
\( 1 \) |
\(5.366838\) |
\(0.350941\) |
\(3.766882\) |
$[1256652,52204481283,17891676439496172,14280]$ |
$[1256652,30995939524,838652756430720,23286599174677950716,114240]$ |
$[16322019979578992366124730896/595,320367650677941067851565476/595,11592952003636922822112]$ |
$y^2 + (x^2 + 1)y = -51x^6 - 315x^4 - 104x^2 - 9$ |
| 114240.b.114240.1 |
114240.b |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
\( - 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
$2$ |
$5$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(4.237720\) |
\(3.130022\) |
\(1.658020\) |
$[1372800,230397,105393832080,14280]$ |
$[1372800,78524006402,5988740824631040,513830955658038681599,114240]$ |
$[5078846877868228608000000000/119,211618205972373394022400000/119,98794294687365488640000]$ |
$y^2 + x^2y = -17x^6 - 94x^4 - 172x^2 - 105$ |
| 114240.c.114240.1 |
114240.c |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(3.610941\) |
\(0.902735\) |
$[1372800,230397,105393832080,14280]$ |
$[1372800,78524006402,5988740824631040,513830955658038681599,114240]$ |
$[5078846877868228608000000000/119,211618205972373394022400000/119,98794294687365488640000]$ |
$y^2 + x^2y = 17x^6 - 94x^4 + 172x^2 - 105$ |
| 114240.d.114240.1 |
114240.d |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
$0$ |
$6$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$256$ |
\( 1 \) |
\(1.000000\) |
\(0.165182\) |
\(2.642912\) |
$[1256652,52204481283,17891676439496172,14280]$ |
$[1256652,30995939524,838652756430720,23286599174677950716,114240]$ |
$[16322019979578992366124730896/595,320367650677941067851565476/595,11592952003636922822112]$ |
$y^2 + (x^2 + 1)y = 51x^6 - 315x^4 + 103x^2 - 9$ |
