The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000
| 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 |
Intrinsic torsion order |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
Manin constant |
| 20096.a1 |
20096b1 |
20096.a |
20096b |
$1$ |
$1$ |
\( 2^{7} \cdot 157 \) |
\( - 2^{8} \cdot 157 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$628$ |
$2$ |
$0$ |
$1.239675009$ |
$1$ |
|
$2$ |
$1344$ |
$-0.434252$ |
$-16000/157$ |
$0.66414$ |
$1.82811$ |
$1$ |
$[0, 1, 0, -3, -11]$ |
\(y^2=x^3+x^2-3x-11\) |
628.2.0.? |
$[(3, 4)]$ |
$1$ |
| 20096.b1 |
20096d1 |
20096.b |
20096d |
$1$ |
$1$ |
\( 2^{7} \cdot 157 \) |
\( - 2^{14} \cdot 157 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$628$ |
$2$ |
$0$ |
$0.849253360$ |
$1$ |
|
$2$ |
$2688$ |
$-0.087678$ |
$-16000/157$ |
$0.66414$ |
$2.24785$ |
$1$ |
$[0, 1, 0, -13, 75]$ |
\(y^2=x^3+x^2-13x+75\) |
628.2.0.? |
$[(1, 8)]$ |
$1$ |
| 20096.c1 |
20096c1 |
20096.c |
20096c |
$1$ |
$1$ |
\( 2^{7} \cdot 157 \) |
\( - 2^{14} \cdot 157 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$628$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$2688$ |
$-0.087678$ |
$-16000/157$ |
$0.66414$ |
$2.24785$ |
$1$ |
$[0, -1, 0, -13, -75]$ |
\(y^2=x^3-x^2-13x-75\) |
628.2.0.? |
$[ ]$ |
$1$ |
| 20096.d1 |
20096a1 |
20096.d |
20096a |
$1$ |
$1$ |
\( 2^{7} \cdot 157 \) |
\( - 2^{8} \cdot 157 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$628$ |
$2$ |
$0$ |
$1.255854529$ |
$1$ |
|
$2$ |
$1344$ |
$-0.434252$ |
$-16000/157$ |
$0.66414$ |
$1.82811$ |
$1$ |
$[0, -1, 0, -3, 11]$ |
\(y^2=x^3-x^2-3x+11\) |
628.2.0.? |
$[(2, 3)]$ |
$1$ |
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