Atkin-Lehner |
2- 3+ 11- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
31152q |
Isogeny class |
Conductor |
31152 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
34560 |
Modular degree for the optimal curve |
Δ |
50529042432 = 218 · 33 · 112 · 59 |
Discriminant |
Eigenvalues |
2- 3+ -4 0 11- 2 -8 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1000,-5264] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:22:1] |
Generators of the group modulo torsion |
j |
27027009001/12336192 |
j-invariant |
L |
2.6865899068052 |
L(r)(E,1)/r! |
Ω |
0.88644169238877 |
Real period |
R |
1.5153788060022 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3894e1 124608de1 93456bm1 |
Quadratic twists by: -4 8 -3 |