| 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 |
| 128.a1 |
128a2 |
128.a |
128a |
$2$ |
$2$ |
\( 2^{7} \) |
\( 2^{13} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
32.96.0.104 |
2B |
$32$ |
$96$ |
$0$ |
$0.216165582$ |
$1$ |
|
$11$ |
$8$ |
$-0.509856$ |
$10976$ |
$0.88842$ |
$3.77458$ |
$[0, 1, 0, -9, 7]$ |
\(y^2=x^3+x^2-9x+7\) |
2.3.0.a.1, 4.6.0.b.1, 8.24.0-8.h.1.1, 16.48.0-16.c.1.4, 32.96.0-32.c.1.4 |
$[(3, 4)]$ |
| 128.a2 |
128a1 |
128.a |
128a |
$2$ |
$2$ |
\( 2^{7} \) |
\( - 2^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
32.96.0.27 |
2B |
$32$ |
$96$ |
$0$ |
$0.432331164$ |
$1$ |
|
$7$ |
$4$ |
$-0.856430$ |
$128$ |
$0.96902$ |
$2.66341$ |
$[0, 1, 0, 1, 1]$ |
\(y^2=x^3+x^2+x+1\) |
2.3.0.a.1, 4.12.0-4.a.1.1, 8.24.0-8.g.1.1, 16.48.0-16.a.1.2, 32.96.0-32.a.1.2 |
$[(0, 1)]$ |
| 128.b1 |
128b2 |
128.b |
128b |
$2$ |
$2$ |
\( 2^{7} \) |
\( 2^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
32.96.0.108 |
2B |
$32$ |
$96$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$-0.856430$ |
$10976$ |
$0.88842$ |
$2.91744$ |
$[0, 1, 0, -2, -2]$ |
\(y^2=x^3+x^2-2x-2\) |
2.3.0.a.1, 4.6.0.b.1, 8.24.0-8.h.1.2, 16.48.0-16.c.1.3, 32.96.0-32.c.1.3 |
$[]$ |
| 128.b2 |
128b1 |
128.b |
128b |
$2$ |
$2$ |
\( 2^{7} \) |
\( - 2^{14} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
32.96.0.3 |
2B |
$32$ |
$96$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$8$ |
$-0.509856$ |
$128$ |
$0.96902$ |
$3.52055$ |
$[0, 1, 0, 3, -5]$ |
\(y^2=x^3+x^2+3x-5\) |
2.3.0.a.1, 4.12.0-4.a.1.2, 8.24.0-8.g.1.2, 16.48.0-16.a.1.1, 32.96.0-32.a.1.1 |
$[]$ |
| 128.c1 |
128c2 |
128.c |
128c |
$2$ |
$2$ |
\( 2^{7} \) |
\( 2^{13} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
32.96.0.102 |
2B |
$32$ |
$96$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$8$ |
$-0.509856$ |
$10976$ |
$0.88842$ |
$3.77458$ |
$[0, -1, 0, -9, -7]$ |
\(y^2=x^3-x^2-9x-7\) |
2.3.0.a.1, 4.6.0.b.1, 8.24.0-8.h.1.1, 16.48.0-16.c.1.2, 32.96.0-32.c.1.2 |
$[]$ |
| 128.c2 |
128c1 |
128.c |
128c |
$2$ |
$2$ |
\( 2^{7} \) |
\( - 2^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
32.96.0.25 |
2B |
$32$ |
$96$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$4$ |
$-0.856430$ |
$128$ |
$0.96902$ |
$2.66341$ |
$[0, -1, 0, 1, -1]$ |
\(y^2=x^3-x^2+x-1\) |
2.3.0.a.1, 4.12.0-4.a.1.1, 8.24.0-8.g.1.1, 16.48.0-16.a.1.3, 32.96.0-32.a.1.3 |
$[]$ |
| 128.d1 |
128d2 |
128.d |
128d |
$2$ |
$2$ |
\( 2^{7} \) |
\( 2^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
32.96.0.106 |
2B |
$32$ |
$96$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$-0.856430$ |
$10976$ |
$0.88842$ |
$2.91744$ |
$[0, -1, 0, -2, 2]$ |
\(y^2=x^3-x^2-2x+2\) |
2.3.0.a.1, 4.6.0.b.1, 8.24.0-8.h.1.2, 16.48.0-16.c.1.1, 32.96.0-32.c.1.1 |
$[]$ |
| 128.d2 |
128d1 |
128.d |
128d |
$2$ |
$2$ |
\( 2^{7} \) |
\( - 2^{14} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
32.96.0.1 |
2B |
$32$ |
$96$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$8$ |
$-0.509856$ |
$128$ |
$0.96902$ |
$3.52055$ |
$[0, -1, 0, 3, 5]$ |
\(y^2=x^3-x^2+3x+5\) |
2.3.0.a.1, 4.12.0-4.a.1.2, 8.24.0-8.g.1.2, 16.48.0-16.a.1.4, 32.96.0-32.a.1.4 |
$[]$ |
