| 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 |
| 50.a1 |
50a2 |
50.a |
50a |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2^{3} \cdot 5^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.8.0.2, 5.24.0.4 |
3B.1.2, 5B.1.3 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$0$ |
$6$ |
$-0.176793$ |
$-349938025/8$ |
$1.05078$ |
$6.67457$ |
$[1, 0, 1, -126, -552]$ |
\(y^2+xy+y=x^3-126x-552\) |
3.8.0-3.a.1.1, 5.24.0-5.a.2.1, 8.2.0.a.1, 15.192.1-15.a.1.1, 24.16.0-24.a.1.6, $\ldots$ |
$[]$ |
| 50.a2 |
50a3 |
50.a |
50a |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2^{5} \cdot 5^{8} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.8.0.1, 5.24.0.2 |
3B.1.1, 5B.1.4 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$2$ |
$10$ |
$0.078619$ |
$-121945/32$ |
$0.94334$ |
$6.38053$ |
$[1, 0, 1, -76, 298]$ |
\(y^2+xy+y=x^3-76x+298\) |
3.8.0-3.a.1.2, 5.24.0-5.a.1.1, 8.2.0.a.1, 15.192.1-15.a.4.4, 24.16.0-24.a.1.8, $\ldots$ |
$[]$ |
| 50.a3 |
50a1 |
50.a |
50a |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2 \cdot 5^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.8.0.1, 5.24.0.4 |
3B.1.1, 5B.1.3 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.726100$ |
$-25/2$ |
$1.09044$ |
$3.73025$ |
$[1, 0, 1, -1, -2]$ |
\(y^2+xy+y=x^3-x-2\) |
3.8.0-3.a.1.2, 5.24.0-5.a.2.1, 8.2.0.a.1, 15.192.1-15.a.2.3, 24.16.0-24.a.1.8, $\ldots$ |
$[]$ |
| 50.a4 |
50a4 |
50.a |
50a |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.8.0.2, 5.24.0.2 |
3B.1.2, 5B.1.4 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$0$ |
$30$ |
$0.627926$ |
$46969655/32768$ |
$1.06296$ |
$7.80683$ |
$[1, 0, 1, 549, -2202]$ |
\(y^2+xy+y=x^3+549x-2202\) |
3.8.0-3.a.1.1, 5.24.0-5.a.1.1, 8.2.0.a.1, 15.192.1-15.a.3.2, 24.16.0-24.a.1.6, $\ldots$ |
$[]$ |
| 50.b1 |
50b4 |
50.b |
50b |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2^{3} \cdot 5^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.4.0.1, 5.24.0.3 |
3B, 5B.1.2 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$0$ |
$30$ |
$0.627926$ |
$-349938025/8$ |
$1.05078$ |
$9.14302$ |
$[1, 1, 1, -3138, -68969]$ |
\(y^2+xy+y=x^3+x^2-3138x-68969\) |
3.4.0.a.1, 5.24.0-5.a.2.2, 8.2.0.a.1, 15.192.1-15.a.1.3, 24.8.0.a.1, $\ldots$ |
$[]$ |
| 50.b2 |
50b3 |
50.b |
50b |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2 \cdot 5^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.4.0.1, 5.24.0.3 |
3B, 5B.1.2 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$0$ |
$10$ |
$0.078619$ |
$-25/2$ |
$1.09044$ |
$6.19870$ |
$[1, 1, 1, -13, -219]$ |
\(y^2+xy+y=x^3+x^2-13x-219\) |
3.4.0.a.1, 5.24.0-5.a.2.2, 8.2.0.a.1, 15.192.1-15.a.2.4, 24.8.0.a.1, $\ldots$ |
$[]$ |
| 50.b3 |
50b1 |
50.b |
50b |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2^{5} \cdot 5^{2} \) |
$0$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.4.0.1, 5.24.0.1 |
3B, 5B.1.1 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$4$ |
$2$ |
$-0.726100$ |
$-121945/32$ |
$0.94334$ |
$3.91208$ |
$[1, 1, 1, -3, 1]$ |
\(y^2+xy+y=x^3+x^2-3x+1\) |
3.4.0.a.1, 5.24.0-5.a.1.2, 8.2.0.a.1, 15.192.1-15.a.4.3, 24.8.0.a.1, $\ldots$ |
$[]$ |
| 50.b4 |
50b2 |
50.b |
50b |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{2} \) |
$0$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.4.0.1, 5.24.0.1 |
3B, 5B.1.1 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$4$ |
$6$ |
$-0.176793$ |
$46969655/32768$ |
$1.06296$ |
$5.33839$ |
$[1, 1, 1, 22, -9]$ |
\(y^2+xy+y=x^3+x^2+22x-9\) |
3.4.0.a.1, 5.24.0-5.a.1.2, 8.2.0.a.1, 15.192.1-15.a.3.1, 24.8.0.a.1, $\ldots$ |
$[]$ |
