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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
Manin constant |
| 36.a1 |
36a4 |
36.a |
36a |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-12$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$1$ |
$6$ |
$0.080464$ |
$54000$ |
$1.02720$ |
$7.34737$ |
$[0, 0, 0, -135, -594]$ |
\(y^2=x^3-135x-594\) |
|
$[ ]$ |
$1$ |
| 36.a2 |
36a2 |
36.a |
36a |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{3} \) |
$0$ |
$\Z/6\Z$ |
$\Q(\sqrt{-3})$ |
$-12$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$5$ |
$2$ |
$-0.468842$ |
$54000$ |
$1.02720$ |
$5.50793$ |
$[0, 0, 0, -15, 22]$ |
\(y^2=x^3-15x+22\) |
|
$[ ]$ |
$1$ |
| 36.a3 |
36a3 |
36.a |
36a |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2, 3$ |
16.192.9.83, 27.648.18.4 |
2B, 3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$1$ |
$3$ |
$-0.266109$ |
$0$ |
|
$5.61315$ |
$[0, 0, 0, 0, -27]$ |
\(y^2=x^3-27\) |
|
$[ ]$ |
$1$ |
| 36.a4 |
36a1 |
36.a |
36a |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{3} \) |
$0$ |
$\Z/6\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2, 3$ |
16.192.9.83, 27.648.18.1 |
2B, 3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$5$ |
$1$ |
$-0.815415$ |
$0$ |
|
$3.77371$ |
$[0, 0, 0, 0, 1]$ |
\(y^2=x^3+1\) |
|
$[ ]$ |
$1$ |
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