| 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 |
| 21904.a.21904.1 |
21904.a |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{4} \cdot 37^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.30.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.102223\) |
\(5.948582\) |
\(0.608081\) |
$[72,4245,4383,-2738]$ |
$[72,-2614,53568,-744025,-21904]$ |
$[-\frac{120932352}{1369},\frac{60979392}{1369},-\frac{17356032}{1369}]$ |
$y^2 + y = -x^6 - 3x^4 - 2x^2$ |
| 21904.b.21904.1 |
21904.b |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{4} \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$10$ |
$0$ |
2.120.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.039046\) |
\(16.464272\) |
\(0.642859\) |
$[312,789,80049,2738]$ |
$[312,3530,44736,374183,21904]$ |
$[\frac{184779159552}{1369},\frac{6700674240}{1369},\frac{272173824}{1369}]$ |
$y^2 + y = -x^6 + 3x^4 - 2x^2$ |
| 21904.c.21904.1 |
21904.c |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{4} \cdot 37^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.120.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.583231\) |
\(23.045086\) |
\(1.493401\) |
$[376,2005,226729,2738]$ |
$[376,4554,61120,560551,21904]$ |
$[\frac{469698574336}{1369},\frac{15129918144}{1369},\frac{540056320}{1369}]$ |
$y^2 + y = -x^6 + 4x^4 - 2x^2$ |
| 21904.d.21904.1 |
21904.d |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{4} \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.30.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.059620\) |
\(10.562417\) |
\(0.629726\) |
$[120,213,14793,2738]$ |
$[120,458,-4416,-184921,21904]$ |
$[\frac{1555200000}{1369},\frac{49464000}{1369},-\frac{3974400}{1369}]$ |
$y^2 + x^3y = x^4 - 1$ |
| 21904.e.350464.1 |
21904.e |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{8} \cdot 37^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.051730\) |
\(1.253233\) |
$[302,5032,388574,1369]$ |
$[604,1782,-1772,-1061453,350464]$ |
$[\frac{314010903004}{1369},\frac{3067669341}{2738},-\frac{10100843}{5476}]$ |
$y^2 = x^5 + 3x^4 - 11x^3 + 8x^2 - x$ |
| 21904.f.810448.1 |
21904.f |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{4} \cdot 37^{3} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.120.4, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(4.326207\) |
\(1.442069\) |
$[8440,111445,301327705,101306]$ |
$[8440,2893770,1298031040,645369291175,810448]$ |
$[\frac{2676654093126400000}{50653},\frac{2938797374040000}{1369},\frac{4221303136000}{37}]$ |
$y^2 + x^3y = -5x^4 + 25x^2 - 37$ |
