| Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 408.a1 |
408c1 |
408.a |
408c |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 17 \) |
\( - 2^{8} \cdot 3^{3} \cdot 17^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$240$ |
$0.606012$ |
$57530252288/38336139$ |
$1.04113$ |
$5.04399$ |
$[0, -1, 0, 511, -1899]$ |
\(y^2=x^3-x^2+511x-1899\) |
102.2.0.? |
$[ ]$ |
| 408.b1 |
408d1 |
408.b |
408d |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 17 \) |
\( - 2^{8} \cdot 3^{5} \cdot 17 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$0.035837594$ |
$1$ |
|
$16$ |
$80$ |
$-0.154003$ |
$-2249728/4131$ |
$0.90547$ |
$3.59327$ |
$[0, 1, 0, -17, 51]$ |
\(y^2=x^3+x^2-17x+51\) |
102.2.0.? |
$[(7, 18)]$ |
| 408.c1 |
408a1 |
408.c |
408a |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 17 \) |
\( 2^{10} \cdot 3^{2} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$32$ |
$-0.193734$ |
$12194500/153$ |
$0.87537$ |
$3.86740$ |
$[0, 1, 0, -48, -144]$ |
\(y^2=x^3+x^2-48x-144\) |
2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.? |
$[ ]$ |
| 408.c2 |
408a2 |
408.c |
408a |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 17 \) |
\( - 2^{11} \cdot 3^{4} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$64$ |
$0.152840$ |
$-31250/23409$ |
$1.14865$ |
$4.18231$ |
$[0, 1, 0, -8, -336]$ |
\(y^2=x^3+x^2-8x-336\) |
2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.? |
$[ ]$ |
| 408.d1 |
408b3 |
408.d |
408b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 17 \) |
\( 2^{11} \cdot 3^{8} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.102 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$256$ |
$0.452304$ |
$22994537186/111537$ |
$1.03807$ |
$5.23736$ |
$[0, 1, 0, -752, -8160]$ |
\(y^2=x^3+x^2-752x-8160\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 68.12.0-4.c.1.1, 136.48.0.? |
$[ ]$ |
| 408.d2 |
408b2 |
408.d |
408b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 17 \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.4 |
2Cs |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$128$ |
$0.105731$ |
$40873252/23409$ |
$1.13826$ |
$4.06860$ |
$[0, 1, 0, -72, 0]$ |
\(y^2=x^3+x^2-72x\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 68.24.0-68.b.1.1, 136.48.0.? |
$[ ]$ |
| 408.d3 |
408b1 |
408.d |
408b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 17 \) |
\( 2^{8} \cdot 3^{2} \cdot 17 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.53 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$64$ |
$-0.240843$ |
$61918288/153$ |
$0.87866$ |
$3.90708$ |
$[0, 1, 0, -52, 128]$ |
\(y^2=x^3+x^2-52x+128\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 34.6.0.a.1, 68.24.0-68.g.1.2, $\ldots$ |
$[ ]$ |
| 408.d4 |
408b4 |
408.d |
408b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 17 \) |
\( - 2^{11} \cdot 3^{2} \cdot 17^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.59 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$256$ |
$0.452304$ |
$1285471294/751689$ |
$1.05433$ |
$4.75757$ |
$[0, 1, 0, 288, 288]$ |
\(y^2=x^3+x^2+288x+288\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 136.48.0.? |
$[ ]$ |
