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 |
| 129.a1 |
129a1 |
129.a |
129a |
$1$ |
$1$ |
\( 3 \cdot 43 \) |
\( - 3^{4} \cdot 43 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$86$ |
$2$ |
$0$ |
$0.099959152$ |
$1$ |
|
$8$ |
$8$ |
$-0.467113$ |
$-799178752/3483$ |
$0.95634$ |
$4.21963$ |
$1$ |
$[0, -1, 1, -19, 39]$ |
\(y^2+y=x^3-x^2-19x+39\) |
86.2.0.? |
$[(1, 4)]$ |
$1$ |
| 129.b1 |
129b3 |
129.b |
129b |
$4$ |
$4$ |
\( 3 \cdot 43 \) |
\( 3^{12} \cdot 43 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.7 |
2B |
$1032$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$30$ |
$0.216827$ |
$1616855892553/22851963$ |
$1.05806$ |
$5.78448$ |
$1$ |
$[1, 0, 1, -245, 1433]$ |
\(y^2+xy+y=x^3-245x+1433\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 172.24.0.?, 1032.48.0.? |
$[ ]$ |
$1$ |
| 129.b2 |
129b1 |
129.b |
129b |
$4$ |
$4$ |
\( 3 \cdot 43 \) |
\( 3^{6} \cdot 43^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.1 |
2Cs |
$516$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$15$ |
$-0.129747$ |
$2845178713/1347921$ |
$0.95310$ |
$4.47937$ |
$1$ |
$[1, 0, 1, -30, -29]$ |
\(y^2+xy+y=x^3-30x-29\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 172.24.0.?, 516.48.0.? |
$[ ]$ |
$1$ |
| 129.b3 |
129b2 |
129.b |
129b |
$4$ |
$4$ |
\( 3 \cdot 43 \) |
\( 3^{3} \cdot 43 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$1032$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$30$ |
$-0.476320$ |
$1630532233/1161$ |
$0.91317$ |
$4.36481$ |
$2$ |
$[1, 0, 1, -25, -49]$ |
\(y^2+xy+y=x^3-25x-49\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.z.1.4, $\ldots$ |
$[ ]$ |
$2$ |
| 129.b4 |
129b4 |
129.b |
129b |
$4$ |
$4$ |
\( 3 \cdot 43 \) |
\( - 3^{3} \cdot 43^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.8 |
2B |
$1032$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$30$ |
$0.216827$ |
$129784785047/92307627$ |
$0.98681$ |
$5.26546$ |
$2$ |
$[1, 0, 1, 105, -191]$ |
\(y^2+xy+y=x^3+105x-191\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 344.24.0.?, $\ldots$ |
$[ ]$ |
$1$ |
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