Atkin-Lehner |
2- 3+ 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312bw |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-120127488 = -1 · 216 · 3 · 13 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -2 1 3 13+ 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,31,513] |
[a1,a2,a3,a4,a6] |
Generators |
[7:32:1] |
Generators of the group modulo torsion |
j |
48668/1833 |
j-invariant |
L |
5.7133535033794 |
L(r)(E,1)/r! |
Ω |
1.408766408659 |
Real period |
R |
2.0277859528249 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000060908 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312x1 29328g1 |
Quadratic twists by: -4 8 |