| 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 |
| 238.a1 |
238b2 |
238.a |
238b |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 17 \) |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.6 |
2B |
$952$ |
$12$ |
$0$ |
$0.320983454$ |
$1$ |
|
$6$ |
$16$ |
$-0.451278$ |
$60698457/28322$ |
$0.89781$ |
$3.27495$ |
$[1, -1, 0, -8, 6]$ |
\(y^2+xy=x^3-x^2-8x+6\) |
2.3.0.a.1, 8.6.0.b.1, 476.6.0.?, 952.12.0.? |
$[(5, 6)]$ |
| 238.a2 |
238b1 |
238.a |
238b |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 17 \) |
\( - 2^{2} \cdot 7 \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.1 |
2B |
$952$ |
$12$ |
$0$ |
$0.641966908$ |
$1$ |
|
$7$ |
$8$ |
$-0.797852$ |
$658503/476$ |
$0.89406$ |
$2.44829$ |
$[1, -1, 0, 2, 0]$ |
\(y^2+xy=x^3-x^2+2x\) |
2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.? |
$[(1, 1)]$ |
| 238.b1 |
238e2 |
238.b |
238e |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 17 \) |
\( 2^{5} \cdot 7^{2} \cdot 17^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.6 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$160$ |
$0.247834$ |
$234770924809/130960928$ |
$0.97956$ |
$4.78446$ |
$[1, 1, 0, -128, -160]$ |
\(y^2+xy=x^3+x^2-128x-160\) |
2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1 |
$[]$ |
| 238.b2 |
238e1 |
238.b |
238e |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 17 \) |
\( - 2^{10} \cdot 7 \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.1 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$80$ |
$-0.098739$ |
$3449795831/2071552$ |
$0.94689$ |
$4.01325$ |
$[1, 1, 0, 32, 0]$ |
\(y^2+xy=x^3+x^2+32x\) |
2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1 |
$[]$ |
| 238.c1 |
238a2 |
238.c |
238a |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 17 \) |
\( 2^{7} \cdot 7^{4} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.6 |
2B |
$136$ |
$12$ |
$0$ |
$0.053370368$ |
$1$ |
|
$20$ |
$224$ |
$0.405446$ |
$37936442980801/88817792$ |
$0.95838$ |
$5.71370$ |
$[1, 0, 0, -700, 7056]$ |
\(y^2+xy=x^3-700x+7056\) |
2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.? |
$[(14, 0)]$ |
| 238.c2 |
238a1 |
238.c |
238a |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 17 \) |
\( 2^{14} \cdot 7^{2} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.1 |
2B |
$136$ |
$12$ |
$0$ |
$0.106740737$ |
$1$ |
|
$17$ |
$112$ |
$0.058872$ |
$23912763841/13647872$ |
$0.98171$ |
$4.36705$ |
$[1, 0, 0, -60, 16]$ |
\(y^2+xy=x^3-60x+16\) |
2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.? |
$[(-4, 16)]$ |
| 238.d1 |
238c3 |
238.d |
238c |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 17 \) |
\( 2 \cdot 7^{2} \cdot 17^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.58 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$64$ |
$0.279129$ |
$16342588257633/8185058$ |
$1.11945$ |
$5.55981$ |
$[1, -1, 1, -529, -4545]$ |
\(y^2+xy+y=x^3-x^2-529x-4545\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 136.48.0.? |
$[]$ |
| 238.d2 |
238c2 |
238.d |
238c |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 17 \) |
\( 2^{2} \cdot 7^{4} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.1 |
2Cs |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$32$ |
$-0.067444$ |
$6403769793/2775556$ |
$1.13395$ |
$4.12629$ |
$[1, -1, 1, -39, -37]$ |
\(y^2+xy+y=x^3-x^2-39x-37\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 68.24.0-68.b.1.1, 136.48.0.? |
$[]$ |
| 238.d3 |
238c1 |
238.d |
238c |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 17 \) |
\( 2^{4} \cdot 7^{2} \cdot 17 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.50 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$16$ |
$-0.414018$ |
$721734273/13328$ |
$0.89265$ |
$3.72737$ |
$[1, -1, 1, -19, 35]$ |
\(y^2+xy+y=x^3-x^2-19x+35\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 34.6.0.a.1, 68.24.0-68.g.1.2, $\ldots$ |
$[]$ |
| 238.d4 |
238c4 |
238.d |
238c |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 17 \) |
\( - 2 \cdot 7^{8} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.103 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$64$ |
$0.279129$ |
$250404380127/196003234$ |
$0.98833$ |
$4.79624$ |
$[1, -1, 1, 131, -377]$ |
\(y^2+xy+y=x^3-x^2+131x-377\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 68.12.0-4.c.1.1, 136.48.0.? |
$[]$ |
| 238.e1 |
238d2 |
238.e |
238d |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 17 \) |
\( 2 \cdot 7^{4} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.6 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$32$ |
$-0.131603$ |
$2433138625/1387778$ |
$0.96221$ |
$3.94945$ |
$[1, 1, 1, -28, -5]$ |
\(y^2+xy+y=x^3+x^2-28x-5\) |
2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.? |
$[]$ |
| 238.e2 |
238d1 |
238.e |
238d |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 17 \) |
\( 2^{2} \cdot 7^{2} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.1 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$-0.478177$ |
$647214625/3332$ |
$0.86431$ |
$3.70745$ |
$[1, 1, 1, -18, -37]$ |
\(y^2+xy+y=x^3+x^2-18x-37\) |
2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.? |
$[]$ |
