| 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 |
| 414.a1 |
414c3 |
414.a |
414c |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( 2 \cdot 3^{14} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$552$ |
$48$ |
$0$ |
$1.908014024$ |
$1$ |
|
$4$ |
$256$ |
$0.604321$ |
$1666957239793/301806$ |
$1.06466$ |
$5.76410$ |
$[1, -1, 0, -2223, -39785]$ |
\(y^2+xy=x^3-x^2-2223x-39785\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 24.24.0-8.p.1.5, 184.24.0.?, $\ldots$ |
$[(-27, 16)]$ |
| 414.a2 |
414c4 |
414.a |
414c |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( 2 \cdot 3^{8} \cdot 23^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.15 |
2B |
$552$ |
$48$ |
$0$ |
$0.477003506$ |
$1$ |
|
$8$ |
$256$ |
$0.604321$ |
$135559106353/5037138$ |
$0.97631$ |
$5.34767$ |
$[1, -1, 0, -963, 11371]$ |
\(y^2+xy=x^3-x^2-963x+11371\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 12.12.0-4.c.1.1, 24.24.0-8.k.1.1, $\ldots$ |
$[(15, 4)]$ |
| 414.a3 |
414c2 |
414.a |
414c |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{10} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.3 |
2Cs |
$552$ |
$48$ |
$0$ |
$0.954007012$ |
$1$ |
|
$12$ |
$128$ |
$0.257747$ |
$545338513/171396$ |
$0.94447$ |
$4.43232$ |
$[1, -1, 0, -153, -455]$ |
\(y^2+xy=x^3-x^2-153x-455\) |
2.6.0.a.1, 8.12.0.a.1, 12.12.0-2.a.1.1, 24.24.0-8.a.1.2, 92.12.0.?, $\ldots$ |
$[(-4, -7)]$ |
| 414.a4 |
414c1 |
414.a |
414c |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( - 2^{4} \cdot 3^{8} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$552$ |
$48$ |
$0$ |
$0.477003506$ |
$1$ |
|
$9$ |
$64$ |
$-0.088827$ |
$2924207/3312$ |
$0.89878$ |
$3.56467$ |
$[1, -1, 0, 27, -59]$ |
\(y^2+xy=x^3-x^2+27x-59\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 12.12.0-4.c.1.2, 24.24.0-8.p.1.8, $\ldots$ |
$[(5, 11)]$ |
| 414.b1 |
414d2 |
414.b |
414d |
$2$ |
$2$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( 2^{5} \cdot 3^{6} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$184$ |
$12$ |
$0$ |
$0.198060968$ |
$1$ |
|
$12$ |
$320$ |
$0.457397$ |
$545138290809/16928$ |
$1.08081$ |
$5.57861$ |
$[1, -1, 1, -1532, 23455]$ |
\(y^2+xy+y=x^3-x^2-1532x+23455\) |
2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.? |
$[(25, 5)]$ |
| 414.b2 |
414d1 |
414.b |
414d |
$2$ |
$2$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( - 2^{10} \cdot 3^{6} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$184$ |
$12$ |
$0$ |
$0.099030484$ |
$1$ |
|
$19$ |
$160$ |
$0.110824$ |
$-116930169/23552$ |
$1.03422$ |
$4.22635$ |
$[1, -1, 1, -92, 415]$ |
\(y^2+xy+y=x^3-x^2-92x+415\) |
2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.? |
$[(1, 17)]$ |
| 414.c1 |
414a4 |
414.c |
414a |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( 2^{6} \cdot 3^{7} \cdot 23^{6} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$276$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$4$ |
$768$ |
$1.245316$ |
$50591419971625/28422890688$ |
$1.07125$ |
$6.33046$ |
$[1, -1, 1, -6935, -36241]$ |
\(y^2+xy+y=x^3-x^2-6935x-36241\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 12.48.0-12.h.1.7, 92.6.0.?, $\ldots$ |
$[]$ |
| 414.c2 |
414a2 |
414.c |
414a |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{9} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$276$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$256$ |
$0.696010$ |
$21081759765625/57132$ |
$1.12484$ |
$6.18519$ |
$[1, -1, 1, -5180, -142189]$ |
\(y^2+xy+y=x^3-x^2-5180x-142189\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 12.48.0-12.h.1.5, 92.6.0.?, $\ldots$ |
$[]$ |
| 414.c3 |
414a1 |
414.c |
414a |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( - 2^{4} \cdot 3^{12} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$276$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$128$ |
$0.349436$ |
$-4956477625/268272$ |
$0.95072$ |
$4.81342$ |
$[1, -1, 1, -320, -2221]$ |
\(y^2+xy+y=x^3-x^2-320x-2221\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 12.48.0-12.i.1.6, 46.6.0.a.1, $\ldots$ |
$[]$ |
| 414.c4 |
414a3 |
414.c |
414a |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( - 2^{12} \cdot 3^{8} \cdot 23^{3} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$276$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$5$ |
$384$ |
$0.898743$ |
$752329532375/448524288$ |
$1.05431$ |
$5.63207$ |
$[1, -1, 1, 1705, -5137]$ |
\(y^2+xy+y=x^3-x^2+1705x-5137\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 12.48.0-12.i.1.8, 46.6.0.a.1, $\ldots$ |
$[]$ |
| 414.d1 |
414b2 |
414.d |
414b |
$2$ |
$2$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( 2 \cdot 3^{7} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$552$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$128$ |
$0.144754$ |
$3463512697/3174$ |
$0.94552$ |
$4.73911$ |
$[1, -1, 1, -284, -1767]$ |
\(y^2+xy+y=x^3-x^2-284x-1767\) |
2.3.0.a.1, 24.6.0.a.1, 92.6.0.?, 552.12.0.? |
$[]$ |
| 414.d2 |
414b1 |
414.d |
414b |
$2$ |
$2$ |
\( 2 \cdot 3^{2} \cdot 23 \) |
\( - 2^{2} \cdot 3^{8} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$552$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$64$ |
$-0.201819$ |
$-389017/828$ |
$0.87759$ |
$3.48596$ |
$[1, -1, 1, -14, -39]$ |
\(y^2+xy+y=x^3-x^2-14x-39\) |
2.3.0.a.1, 24.6.0.d.1, 46.6.0.a.1, 552.12.0.? |
$[]$ |
