Atkin-Lehner |
2+ 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
12272g |
Isogeny class |
Conductor |
12272 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
-26961584 = -1 · 24 · 134 · 59 |
Discriminant |
Eigenvalues |
2+ -1 3 -3 0 13- 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-579,5566] |
[a1,a2,a3,a4,a6] |
Generators |
[10:26:1] |
Generators of the group modulo torsion |
j |
-1343969093632/1685099 |
j-invariant |
L |
4.0813283416391 |
L(r)(E,1)/r! |
Ω |
2.1046613031836 |
Real period |
R |
0.48479633462466 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6136a1 49088l1 110448s1 |
Quadratic twists by: -4 8 -3 |