Atkin-Lehner |
3- 5- 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
52065n |
Isogeny class |
Conductor |
52065 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
44928 |
Modular degree for the optimal curve |
Δ |
13178953125 = 36 · 56 · 13 · 89 |
Discriminant |
Eigenvalues |
-2 3- 5- -1 -2 13+ -1 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-597,-1008] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:62:1] [-13:67:1] |
Generators of the group modulo torsion |
j |
32278933504/18078125 |
j-invariant |
L |
5.3699221210622 |
L(r)(E,1)/r! |
Ω |
1.0379108522077 |
Real period |
R |
0.43114831022012 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5785a1 |
Quadratic twists by: -3 |