Atkin-Lehner |
2- 3- 7+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
71232cu |
Isogeny class |
Conductor |
71232 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
-571731181830144 = -1 · 225 · 38 · 72 · 53 |
Discriminant |
Eigenvalues |
2- 3- 3 7+ -1 4 -3 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-47489,-4161921] |
[a1,a2,a3,a4,a6] |
Generators |
[415:-6912:1] |
Generators of the group modulo torsion |
j |
-45182682230113/2180981376 |
j-invariant |
L |
9.7347064669476 |
L(r)(E,1)/r! |
Ω |
0.16124991245198 |
Real period |
R |
0.94328602238365 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001283 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
71232n1 17808o1 |
Quadratic twists by: -4 8 |