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 |
| 972.a1 |
972d2 |
972.a |
972d |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{5} \) |
\( - 2^{8} \cdot 3^{13} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$2.999367973$ |
$1$ |
|
$2$ |
$324$ |
$0.331144$ |
$0$ |
|
$3.96576$ |
$1$ |
$[0, 0, 0, 0, -972]$ |
\(y^2=x^3-972\) |
|
$[(13, 35)]$ |
$1$ |
| 972.a2 |
972d1 |
972.a |
972d |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{5} \) |
\( - 2^{8} \cdot 3^{7} \) |
$1$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$0.999789324$ |
$1$ |
|
$8$ |
$108$ |
$-0.218162$ |
$0$ |
|
$3.00758$ |
$1$ |
$[0, 0, 0, 0, 36]$ |
\(y^2=x^3+36\) |
|
$[(-3, 3)]$ |
$1$ |
| 972.b1 |
972c2 |
972.b |
972c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{5} \) |
\( - 2^{4} \cdot 3^{13} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$2.444086321$ |
$1$ |
|
$2$ |
$162$ |
$0.100095$ |
$0$ |
|
$3.56273$ |
$1$ |
$[0, 0, 0, 0, -243]$ |
\(y^2=x^3-243\) |
|
$[(7, 10)]$ |
$1$ |
| 972.b2 |
972c1 |
972.b |
972c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{5} \) |
\( - 2^{4} \cdot 3^{7} \) |
$1$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$0.814695440$ |
$1$ |
|
$10$ |
$54$ |
$-0.449211$ |
$0$ |
|
$2.60455$ |
$1$ |
$[0, 0, 0, 0, 9]$ |
\(y^2=x^3+9\) |
|
$[(3, 6)]$ |
$1$ |
| 972.c1 |
972a1 |
972.c |
972a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{5} \) |
\( - 2^{8} \cdot 3^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$54$ |
$-0.401264$ |
$0$ |
|
$2.68818$ |
$1$ |
$[0, 0, 0, 0, -12]$ |
\(y^2=x^3-12\) |
|
$[ ]$ |
$1$ |
| 972.c2 |
972a2 |
972.c |
972a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{5} \) |
\( - 2^{8} \cdot 3^{11} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$162$ |
$0.148042$ |
$0$ |
|
$3.64636$ |
$1$ |
$[0, 0, 0, 0, 324]$ |
\(y^2=x^3+324\) |
|
$[ ]$ |
$1$ |
| 972.d1 |
972b1 |
972.d |
972b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{5} \) |
\( - 2^{4} \cdot 3^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$54$ |
$-0.632313$ |
$0$ |
|
$2.28515$ |
$1$ |
$[0, 0, 0, 0, -3]$ |
\(y^2=x^3-3\) |
|
$[ ]$ |
$1$ |
| 972.d2 |
972b2 |
972.d |
972b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{5} \) |
\( - 2^{4} \cdot 3^{11} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$162$ |
$-0.083007$ |
$0$ |
|
$3.24333$ |
$1$ |
$[0, 0, 0, 0, 81]$ |
\(y^2=x^3+81\) |
|
$[ ]$ |
$1$ |
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