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 |
| 44.a1 |
44a2 |
44.a |
44a |
$2$ |
$3$ |
\( 2^{2} \cdot 11 \) |
\( - 2^{8} \cdot 11^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$66$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$6$ |
$-0.102988$ |
$-199794688/1331$ |
$0.99506$ |
$6.51908$ |
$1$ |
$[0, 1, 0, -77, -289]$ |
\(y^2=x^3+x^2-77x-289\) |
3.8.0-3.a.1.1, 22.2.0.a.1, 66.16.0-66.a.1.1 |
$[ ]$ |
$1$ |
| 44.a2 |
44a1 |
44.a |
44a |
$2$ |
$3$ |
\( 2^{2} \cdot 11 \) |
\( - 2^{8} \cdot 11 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$66$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.652294$ |
$8192/11$ |
$0.84294$ |
$3.91998$ |
$1$ |
$[0, 1, 0, 3, -1]$ |
\(y^2=x^3+x^2+3x-1\) |
3.8.0-3.a.1.2, 22.2.0.a.1, 66.16.0-66.a.1.4 |
$[ ]$ |
$1$ |
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