| 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 |
| 1680.a.16800.1 |
1680.a |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( - 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.090690\) |
\(0.636336\) |
$[404040,44088,5935895700,67200]$ |
$[202020,1700496002,19085068732800,240969733145567999,16800]$ |
$[20029151526577171524000,834544374130868293620,46363176164438078400]$ |
$y^2 + (x^3 + x)y = -x^6 - 18x^4 - 136x^2 - 350$ |
| 1680.b.215040.1 |
1680.b |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( 2^{11} \cdot 3 \cdot 5 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.032776\) |
\(0.629097\) |
$[11352,175353,681849159,26880]$ |
$[11352,5252594,3148904976,2039156389679,215040]$ |
$[\frac{30683910352656528}{35},\frac{2501322958040841}{70},\frac{18870572179701}{10}]$ |
$y^2 + xy = 4x^5 + 25x^4 + 44x^3 + 15x^2 + x$ |
| 1680.c.241920.1 |
1680.c |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( 2^{8} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.725763\) |
\(0.488573\) |
$[182340,50613,3073006935,30240]$ |
$[182340,1385294408,14032351630080,159904599848179184,241920]$ |
$[\frac{5832248478791381977500}{7},\frac{243004434356588125950}{7},1928513067842084400]$ |
$y^2 + (x^2 + 1)y = 135x^6 - 96x^4 + 22x^2 - 2$ |
