| 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 |
| 8192.b.131072.1 |
8192.b |
\( 2^{13} \) |
\( 2^{17} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.540.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(15.683046\) |
\(0.980190\) |
$[64,76,1552,16]$ |
$[256,1920,8192,-397312,131072]$ |
$[8388608,245760,4096]$ |
$y^2 = x^5 - 3x^4 + 6x^2 - 4x$ |
| 102400.b.102400.1 |
102400.b |
\( 2^{12} \cdot 5^{2} \) |
\( - 2^{12} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$2$ |
2.90.3, 3.540.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.797280\) |
\(12.084061\) |
\(2.408596\) |
$[34,-116,-424,400]$ |
$[68,502,-2100,-98701,102400]$ |
$[\frac{1419857}{100},\frac{1233163}{800},-\frac{6069}{64}]$ |
$y^2 = x^5 - x^3 - x$ |
| 186624.d.373248.1 |
186624.d |
\( 2^{8} \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{6} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.60.2, 3.2880.5 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.721206\) |
\(11.730951\) |
\(2.820144\) |
$[32,117,879,-6]$ |
$[192,-1272,-2624,-530448,-373248]$ |
$[-\frac{2097152}{3},\frac{217088}{9},\frac{20992}{81}]$ |
$y^2 + x^3y = 2x^3 + 2$ |
| 262144.a.262144.1 |
262144.a |
\( 2^{18} \) |
\( - 2^{18} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.90.3, 3.3240.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.123513\) |
\(10.883805\) |
\(3.057023\) |
$[4,-14,2,1]$ |
$[32,640,-6144,-151552,262144]$ |
$[128,80,-24]$ |
$y^2 = x^5 - 2x^3 - x$ |
| 262144.d.524288.1 |
262144.d |
\( 2^{18} \) |
\( 2^{19} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathsf{QM}\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3, 3.360.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.658241\) |
\(3.857919\) |
\(3.198681\) |
$[42,-18,-324,2]$ |
$[336,5472,163584,6255360,524288]$ |
$[8168202,\frac{1583631}{4},\frac{281799}{8}]$ |
$y^2 = x^5 - x^4 + 4x^3 - 8x^2 + 5x - 1$ |
| 262144.d.524288.2 |
262144.d |
\( 2^{18} \) |
\( 2^{19} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathsf{QM}\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3, 3.360.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.552747\) |
\(11.573758\) |
\(3.198681\) |
$[42,-18,-324,2]$ |
$[336,5472,163584,6255360,524288]$ |
$[8168202,\frac{1583631}{4},\frac{281799}{8}]$ |
$y^2 = x^5 + x^4 + 4x^3 + 8x^2 + 5x + 1$ |
| 589824.c.589824.1 |
589824.c |
\( 2^{16} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.5, 3.540.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.017767\) |
\(15.387171\) |
\(3.915138\) |
$[196,892,55928,72]$ |
$[784,16096,5888,-63616256,589824]$ |
$[\frac{4519603984}{9},\frac{118354894}{9},\frac{55223}{9}]$ |
$y^2 = x^5 - 2x^4 - 4x^3 + 8x^2 + x - 2$ |
| 589824.c.589824.2 |
589824.c |
\( 2^{16} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.5, 3.540.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(2.035534\) |
\(7.693585\) |
\(3.915138\) |
$[196,892,55928,72]$ |
$[784,16096,5888,-63616256,589824]$ |
$[\frac{4519603984}{9},\frac{118354894}{9},\frac{55223}{9}]$ |
$y^2 = x^5 + 2x^4 - 4x^3 - 8x^2 + x + 2$ |
| 692224.a.692224.1 |
692224.a |
\( 2^{12} \cdot 13^{2} \) |
\( - 2^{12} \cdot 13^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.90.3, 3.540.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(9.748988\) |
\(2.437247\) |
$[14,-404,-3928,-2704]$ |
$[28,1110,19604,-170797,-692224]$ |
$[-\frac{16807}{676},-\frac{190365}{5408},-\frac{1421}{64}]$ |
$y^2 = x^5 - 3x^3 - x$ |
