Atkin-Lehner |
3- 13+ 103+ |
Signs for the Atkin-Lehner involutions |
Class |
12051a |
Isogeny class |
Conductor |
12051 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4992 |
Modular degree for the optimal curve |
Δ |
-2714620311 = -1 · 39 · 13 · 1032 |
Discriminant |
Eigenvalues |
1 3- -2 -2 -4 13+ 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-243,-2840] |
[a1,a2,a3,a4,a6] |
Generators |
[56:368:1] [68:506:1] |
Generators of the group modulo torsion |
j |
-2181825073/3723759 |
j-invariant |
L |
6.6431638743025 |
L(r)(E,1)/r! |
Ω |
0.5712861791684 |
Real period |
R |
5.8142172141925 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4017a1 |
Quadratic twists by: -3 |