| 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 |
| 540.a1 |
540d2 |
540.a |
540d |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{4} \cdot 3^{11} \cdot 5^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$3.716854919$ |
$1$ |
|
$2$ |
$324$ |
$0.426794$ |
$-5267712/125$ |
$1.15142$ |
$4.82783$ |
$[0, 0, 0, -513, -4563]$ |
\(y^2=x^3-513x-4563\) |
3.8.0-3.a.1.1, 30.16.0-30.b.1.2 |
$[(28, 55)]$ |
| 540.a2 |
540d1 |
540.a |
540d |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{4} \cdot 3^{9} \cdot 5 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$1.238951639$ |
$1$ |
|
$10$ |
$108$ |
$-0.122512$ |
$6912/5$ |
$0.69897$ |
$3.41745$ |
$[0, 0, 0, 27, -27]$ |
\(y^2=x^3+27x-27\) |
3.8.0-3.a.1.2, 30.16.0-30.b.1.4 |
$[(1, 1)]$ |
| 540.b1 |
540c1 |
540.b |
540c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{8} \cdot 3^{9} \cdot 5^{2} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$6$ |
$16$ |
$0$ |
$0.505482570$ |
$1$ |
|
$12$ |
$216$ |
$0.409268$ |
$-5971968/25$ |
$1.09044$ |
$4.93398$ |
$[0, 0, 0, -648, 6372]$ |
\(y^2=x^3-648x+6372\) |
3.8.0-3.a.1.2, 6.16.0-6.b.1.2 |
$[(21, 45)]$ |
| 540.b2 |
540c2 |
540.b |
540c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{8} \cdot 3^{11} \cdot 5^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$6$ |
$16$ |
$0$ |
$1.516447711$ |
$1$ |
|
$2$ |
$648$ |
$0.958574$ |
$8429568/15625$ |
$1.06918$ |
$5.46239$ |
$[0, 0, 0, 1512, 33588]$ |
\(y^2=x^3+1512x+33588\) |
3.8.0-3.a.1.1, 6.16.0-6.b.1.1 |
$[(-11, 125)]$ |
| 540.c1 |
540a1 |
540.c |
540a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{4} \cdot 3^{3} \cdot 5 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$36$ |
$-0.411483$ |
$-9199872/5$ |
$0.95440$ |
$3.51328$ |
$[0, 0, 0, -33, 73]$ |
\(y^2=x^3-33x+73\) |
3.8.0-3.a.1.2, 30.16.0-30.b.1.4 |
$[]$ |
| 540.c2 |
540a2 |
540.c |
540a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{4} \cdot 3^{9} \cdot 5^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$108$ |
$0.137823$ |
$6912/125$ |
$1.02720$ |
$3.95936$ |
$[0, 0, 0, 27, 297]$ |
\(y^2=x^3+27x+297\) |
3.8.0-3.a.1.1, 30.16.0-30.b.1.2 |
$[]$ |
| 540.d1 |
540b2 |
540.d |
540b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{4} \cdot 3^{5} \cdot 5^{3} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$0.218874210$ |
$1$ |
|
$18$ |
$108$ |
$-0.122512$ |
$-5267712/125$ |
$1.15142$ |
$3.78013$ |
$[0, 0, 0, -57, 169]$ |
\(y^2=x^3-57x+169\) |
3.8.0-3.a.1.2, 30.16.0-30.b.1.4 |
$[(5, 3)]$ |
| 540.d2 |
540b1 |
540.d |
540b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{4} \cdot 3^{3} \cdot 5 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$0.656622630$ |
$1$ |
|
$2$ |
$36$ |
$-0.671818$ |
$6912/5$ |
$0.69897$ |
$2.36975$ |
$[0, 0, 0, 3, 1]$ |
\(y^2=x^3+3x+1\) |
3.8.0-3.a.1.1, 30.16.0-30.b.1.2 |
$[(0, 1)]$ |
| 540.e1 |
540e1 |
540.e |
540e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{8} \cdot 3^{3} \cdot 5^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$6$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$72$ |
$-0.140038$ |
$-5971968/25$ |
$1.09044$ |
$3.88628$ |
$[0, 0, 0, -72, -236]$ |
\(y^2=x^3-72x-236\) |
3.8.0-3.a.1.1, 6.16.0-6.b.1.1 |
$[]$ |
| 540.e2 |
540e2 |
540.e |
540e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{8} \cdot 3^{5} \cdot 5^{6} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$6$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$216$ |
$0.409268$ |
$8429568/15625$ |
$1.06918$ |
$4.41469$ |
$[0, 0, 0, 168, -1244]$ |
\(y^2=x^3+168x-1244\) |
3.8.0-3.a.1.2, 6.16.0-6.b.1.2 |
$[]$ |
| 540.f1 |
540f2 |
540.f |
540f |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{4} \cdot 3^{9} \cdot 5 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$108$ |
$0.137823$ |
$-9199872/5$ |
$0.95440$ |
$4.56098$ |
$[0, 0, 0, -297, -1971]$ |
\(y^2=x^3-297x-1971\) |
3.8.0-3.a.1.1, 30.16.0-30.b.1.2 |
$[]$ |
| 540.f2 |
540f1 |
540.f |
540f |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
\( - 2^{4} \cdot 3^{3} \cdot 5^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$36$ |
$-0.411483$ |
$6912/125$ |
$1.02720$ |
$2.91166$ |
$[0, 0, 0, 3, -11]$ |
\(y^2=x^3+3x-11\) |
3.8.0-3.a.1.2, 30.16.0-30.b.1.4 |
$[]$ |
