| 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 |
| 475.a1 |
475c2 |
475.a |
475c |
$2$ |
$2$ |
\( 5^{2} \cdot 19 \) |
\( 5^{3} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$380$ |
$12$ |
$0$ |
$0.372858842$ |
$1$ |
|
$8$ |
$32$ |
$-0.326658$ |
$13312053/361$ |
$0.88614$ |
$3.44498$ |
$[1, -1, 1, -25, 52]$ |
\(y^2+xy+y=x^3-x^2-25x+52\) |
2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.? |
$[(4, 0)]$ |
| 475.a2 |
475c1 |
475.a |
475c |
$2$ |
$2$ |
\( 5^{2} \cdot 19 \) |
\( - 5^{3} \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$380$ |
$12$ |
$0$ |
$0.745717685$ |
$1$ |
|
$5$ |
$16$ |
$-0.673232$ |
$27/19$ |
$1.11940$ |
$2.47053$ |
$[1, -1, 1, 0, 2]$ |
\(y^2+xy+y=x^3-x^2+2\) |
2.3.0.a.1, 20.6.0.c.1, 76.6.0.?, 190.6.0.?, 380.12.0.? |
$[(0, 1)]$ |
| 475.b1 |
475a3 |
475.b |
475a |
$3$ |
$9$ |
\( 5^{2} \cdot 19 \) |
\( - 5^{6} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$5130$ |
$1296$ |
$43$ |
$1$ |
$9$ |
$3$ |
$0$ |
$324$ |
$0.838158$ |
$-50357871050752/19$ |
$1.10495$ |
$6.68582$ |
$[0, -1, 1, -19233, -1020257]$ |
\(y^2+y=x^3-x^2-19233x-1020257\) |
3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.1, 27.36.0.a.1, 38.2.0.a.1, $\ldots$ |
$[]$ |
| 475.b2 |
475a2 |
475.b |
475a |
$3$ |
$9$ |
\( 5^{2} \cdot 19 \) |
\( - 5^{6} \cdot 19^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$5130$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$0$ |
$108$ |
$0.288852$ |
$-89915392/6859$ |
$1.03310$ |
$4.55840$ |
$[0, -1, 1, -233, -1382]$ |
\(y^2+y=x^3-x^2-233x-1382\) |
3.12.0.a.1, 9.36.0.b.1, 15.24.0-3.a.1.1, 38.2.0.a.1, 45.72.0-9.b.1.1, $\ldots$ |
$[]$ |
| 475.b3 |
475a1 |
475.b |
475a |
$3$ |
$9$ |
\( 5^{2} \cdot 19 \) |
\( - 5^{6} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$5130$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$0$ |
$36$ |
$-0.260454$ |
$32768/19$ |
$1.31757$ |
$3.25374$ |
$[0, -1, 1, 17, -7]$ |
\(y^2+y=x^3-x^2+17x-7\) |
3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.2, 27.36.0.a.1, 38.2.0.a.1, $\ldots$ |
$[]$ |
| 475.c1 |
475b2 |
475.c |
475b |
$2$ |
$2$ |
\( 5^{2} \cdot 19 \) |
\( 5^{9} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$380$ |
$12$ |
$0$ |
$1.365071063$ |
$1$ |
|
$4$ |
$160$ |
$0.478061$ |
$13312053/361$ |
$0.88614$ |
$5.01177$ |
$[1, -1, 0, -617, 5916]$ |
\(y^2+xy=x^3-x^2-617x+5916\) |
2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.? |
$[(8, 34)]$ |
| 475.c2 |
475b1 |
475.c |
475b |
$2$ |
$2$ |
\( 5^{2} \cdot 19 \) |
\( - 5^{9} \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$380$ |
$12$ |
$0$ |
$2.730142127$ |
$1$ |
|
$3$ |
$80$ |
$0.131487$ |
$27/19$ |
$1.11940$ |
$4.03732$ |
$[1, -1, 0, 8, 291]$ |
\(y^2+xy=x^3-x^2+8x+291\) |
2.3.0.a.1, 20.6.0.c.1, 76.6.0.?, 190.6.0.?, 380.12.0.? |
$[(10, 31)]$ |
