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 |
440509.a.440509.1 |
440509.a |
\( 440509 \) |
\( 440509 \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$24$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.062576\) |
\(17.948640\) |
\(1.123154\) |
$[1028,71593,17110373,56385152]$ |
$[257,-231,14605,925031,440509]$ |
$[1121154893057/440509,-3921130983/440509,964645645/440509]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 5x^3 + 9x + 6$ |
526499.a.526499.1 |
526499.a |
\( 526499 \) |
\( 526499 \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$24$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.065270\) |
\(18.050629\) |
\(1.178168\) |
$[996,116169,26515893,67391872]$ |
$[249,-2257,2253,-1133263,526499]$ |
$[957186876249/526499,-34844127993/526499,139688253/526499]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + 5x^4 - 6x^3$ |
563011.a.563011.1 |
563011.a |
\( 563011 \) |
\( -563011 \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$26$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.073355\) |
\(16.330521\) |
\(1.197933\) |
$[1380,47193,18229677,-72065408]$ |
$[345,2993,30309,374639,-563011]$ |
$[-4887597965625/563011,-122903429625/563011,-3607528725/563011]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + x^3 + 7x^2 + 4x$ |
758059.a.758059.1 |
758059.a |
\( 53 \cdot 14303 \) |
\( 53 \cdot 14303 \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$24$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.094569\) |
\(15.685633\) |
\(1.483377\) |
$[604,82729,30781947,-97031552]$ |
$[151,-2497,-274973,-11938983,-758059]$ |
$[-78502725751/758059,8597048647/758059,6269659373/758059]$ |
$y^2 + (x^3 + x + 1)y = 2x^3 - 3x^2 - 3x + 2$ |
766561.b.766561.1 |
766561.b |
\( 43 \cdot 17827 \) |
\( 43 \cdot 17827 \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$24$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.101614\) |
\(14.960381\) |
\(1.520181\) |
$[1148,63145,26374427,-98119808]$ |
$[287,801,-101837,-7467205,-766561]$ |
$[-1947195170207/766561,-18935562303/766561,8388211853/766561]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + x^3 - 6x + 6$ |
776117.a.776117.1 |
776117.a |
\( 776117 \) |
\( -776117 \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$20$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.185468\) |
\(10.288820\) |
\(1.908246\) |
$[1004,23257,5964515,99342976]$ |
$[251,1656,21328,652748,776117]$ |
$[996250626251/776117,26186743656/776117,1343685328/776117]$ |
$y^2 + (x^3 + x^2 + x)y = 2x^4 + 2x^3 + 3x^2 + 2x + 1$ |
792079.a.792079.1 |
792079.a |
\( 41 \cdot 19319 \) |
\( - 41 \cdot 19319 \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$26$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.084450\) |
\(18.004162\) |
\(1.520457\) |
$[3012,432585,340579413,-101386112]$ |
$[753,5601,28157,-2542245,-792079]$ |
$[-242088902178993/792079,-2391390508977/792079,-15965272413/792079]$ |
$y^2 + (x^3 + x + 1)y = -3x^5 + 7x^4 - 4x^2$ |
806069.a.806069.1 |
806069.a |
\( 11 \cdot 127 \cdot 577 \) |
\( 11 \cdot 127 \cdot 577 \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$24$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.106948\) |
\(14.225673\) |
\(1.521412\) |
$[60,18153,3296763,-103176832]$ |
$[15,-747,-42629,-299361,-806069]$ |
$[-759375/806069,2521125/806069,9591525/806069]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 5x^2 + 5x + 2$ |
864569.a.864569.1 |
864569.a |
\( 17 \cdot 50857 \) |
\( 17 \cdot 50857 \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$24$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.095005\) |
\(14.727530\) |
\(1.399191\) |
$[1380,47193,19940397,110664832]$ |
$[345,2993,6549,-1674661,864569]$ |
$[4887597965625/864569,122903429625/864569,779494725/864569]$ |
$y^2 + (x^3 + x + 1)y = 2x^5 + 2x^4 - 3x^3 - 3x^2$ |
994009.a.994009.1 |
994009.a |
\( 997^{2} \) |
\( 997^{2} \) |
$4$ |
$4$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$18$ |
$0$ |
2.30.2, 3.270.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.142587\) |
\(15.409672\) |
\(2.197213\) |
$[680,14932,2967104,3976036]$ |
$[340,2328,-3656,-1665656,994009]$ |
$[4543542400000/994009,91499712000/994009,-422633600/994009]$ |
$y^2 + x^3y = -4x^4 - 7x^3 - x^2 + 3x + 1$ |