| 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 |
| 4096.a.65536.1 |
4096.a |
\( 2^{12} \) |
\( - 2^{16} \) |
$1$ |
$2$ |
$\Z/8\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$2$ |
2.90.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.432331\) |
\(21.167670\) |
\(0.571965\) |
$[72,894,30654,8]$ |
$[288,-6080,-925696,-75891712,65536]$ |
$[30233088,-2216160,-1171584]$ |
$y^2 + x^3y = -2x^4 + 3x^2 + 4$ |
| 4096.b.65536.1 |
4096.b |
\( 2^{12} \) |
\( - 2^{16} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\mathsf{CM}\) |
✓ |
$J(C_2)$ |
|
✓ |
|
$C_4$ |
$GL(2,3)$ |
$4$ |
$4$ |
2.360.2, 3.6480.22 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(12.689987\) |
\(0.793124\) |
$[20,-20,-40,8]$ |
$[80,480,-1280,-83200,65536]$ |
$[50000,3750,-125]$ |
$y^2 = x^5 - x$ |
| 4096.c.65536.1 |
4096.c |
\( 2^{12} \) |
\( 2^{16} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.2, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.203720\) |
\(0.900465\) |
$[72,894,30654,8]$ |
$[288,-6080,-925696,-75891712,65536]$ |
$[30233088,-2216160,-1171584]$ |
$y^2 + x^3y = 2x^4 + 3x^2 - 4$ |
| 4096.d.524288.1 |
4096.d |
\( 2^{12} \) |
\( - 2^{19} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(7.483901\) |
\(0.935488\) |
$[168,39,2121,2]$ |
$[1344,73600,5275648,418377728,524288]$ |
$[8364238848,340804800,18176256]$ |
$y^2 + x^3y = 2x^4 + 6x^2 + 8$ |
| 4096.e.524288.1 |
4096.e |
\( 2^{12} \) |
\( - 2^{19} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.402544\) |
\(0.925318\) |
$[26,-2,40,2]$ |
$[208,1888,-2304,-1010944,524288]$ |
$[742586,\frac{129623}{4},-\frac{1521}{8}]$ |
$y^2 = x^5 - 2x^4 - 2x^2 - x$ |
| 4096.f.524288.1 |
4096.f |
\( 2^{12} \) |
\( 2^{19} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(5.093799\) |
\(0.636725\) |
$[168,39,2121,2]$ |
$[1344,73600,5275648,418377728,524288]$ |
$[8364238848,340804800,18176256]$ |
$y^2 + x^3y = -2x^4 + 6x^2 - 8$ |
