Atkin-Lehner |
2+ 3+ 5+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
111600c |
Isogeny class |
Conductor |
111600 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
152543250000 = 24 · 39 · 56 · 31 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 4 -2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6750,-212625] |
[a1,a2,a3,a4,a6] |
Generators |
[450753017:4539129778:2924207] |
Generators of the group modulo torsion |
j |
6912000/31 |
j-invariant |
L |
8.0248840629494 |
L(r)(E,1)/r! |
Ω |
0.52685464350347 |
Real period |
R |
15.23168512124 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000035441 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
55800e1 111600d1 4464a1 |
Quadratic twists by: -4 -3 5 |