Atkin-Lehner |
2+ 3+ 5+ 7+ |
Signs for the Atkin-Lehner involutions |
Class |
117600c |
Isogeny class |
Conductor |
117600 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1354752 |
Modular degree for the optimal curve |
Δ |
-806887666368000000 = -1 · 212 · 37 · 56 · 78 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ 2 -1 2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-114333,45746037] |
[a1,a2,a3,a4,a6] |
Generators |
[-9051:183700:27] |
Generators of the group modulo torsion |
j |
-448000/2187 |
j-invariant |
L |
5.9534953238721 |
L(r)(E,1)/r! |
Ω |
0.245339358771 |
Real period |
R |
6.0665921222557 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000065633 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117600gg1 4704y1 117600cv1 |
Quadratic twists by: -4 5 -7 |