| 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 |
| 48.a1 |
48a5 |
48.a |
48a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \) |
\( 2^{11} \cdot 3^{2} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.93 |
2B |
$48$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$8$ |
$0.047795$ |
$3065617154/9$ |
$1.21059$ |
$7.61214$ |
$[0, 1, 0, -384, 2772]$ |
\(y^2=x^3+x^2-384x+2772\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.r.1.2, 16.96.0-16.l.1.2, 24.96.0-24.bf.1.8, $\ldots$ |
$[]$ |
| 48.a2 |
48a2 |
48.a |
48a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \) |
\( 2^{10} \cdot 3 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.150 |
2B |
$48$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$4$ |
$-0.298779$ |
$28756228/3$ |
$1.05617$ |
$6.22697$ |
$[0, 1, 0, -64, -220]$ |
\(y^2=x^3+x^2-64x-220\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 12.24.0-12.h.1.1, 16.96.0-16.bb.2.3, $\ldots$ |
$[]$ |
| 48.a3 |
48a3 |
48.a |
48a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.34 |
2Cs |
$24$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$7$ |
$4$ |
$-0.298779$ |
$1556068/81$ |
$1.03212$ |
$5.47353$ |
$[0, 1, 0, -24, 36]$ |
\(y^2=x^3+x^2-24x+36\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.e.2.1, 24.192.1-24.bl.2.2 |
$[]$ |
| 48.a4 |
48a1 |
48.a |
48a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.53 |
2Cs |
$24$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.645352$ |
$35152/9$ |
$0.97255$ |
$4.13634$ |
$[0, 1, 0, -4, -4]$ |
\(y^2=x^3+x^2-4x-4\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.h.1.2, 12.48.0-12.c.1.3, 24.192.1-24.bu.1.1 |
$[]$ |
| 48.a5 |
48a4 |
48.a |
48a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.142 |
2B |
$48$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$4$ |
$-0.991926$ |
$2048/3$ |
$1.17572$ |
$2.79585$ |
$[0, 1, 0, 1, 0]$ |
\(y^2=x^3+x^2+x\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 8.48.0-8.ba.1.1, 12.24.0-12.g.1.1, $\ldots$ |
$[]$ |
| 48.a6 |
48a6 |
48.a |
48a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \) |
\( - 2^{11} \cdot 3^{8} \) |
$0$ |
$\Z/8\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.155 |
2B |
$48$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$7$ |
$8$ |
$0.047795$ |
$207646/6561$ |
$1.15980$ |
$6.16081$ |
$[0, 1, 0, 16, 180]$ |
\(y^2=x^3+x^2+16x+180\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.96.0-8.m.1.4, 48.192.1-48.w.2.2 |
$[]$ |
