Atkin-Lehner |
2- 3+ 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312bx |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
76800 |
Modular degree for the optimal curve |
Δ |
-36944833536 = -1 · 210 · 310 · 13 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -2 2 4 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,491,-8411] |
[a1,a2,a3,a4,a6] |
Generators |
[23694:251281:216] |
Generators of the group modulo torsion |
j |
12758024192/36078939 |
j-invariant |
L |
4.983592655665 |
L(r)(E,1)/r! |
Ω |
0.5936122629519 |
Real period |
R |
8.3953666936171 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000068938 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117312y1 29328x1 |
Quadratic twists by: -4 8 |