Atkin-Lehner |
2- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75712cu |
Isogeny class |
Conductor |
75712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-138394267648 = -1 · 212 · 7 · 136 |
Discriminant |
Eigenvalues |
2- 2 0 7- -4 13+ -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1127,-10791] |
[a1,a2,a3,a4,a6] |
Generators |
[20415:561536:27] |
Generators of the group modulo torsion |
j |
8000/7 |
j-invariant |
L |
8.8968063498823 |
L(r)(E,1)/r! |
Ω |
0.56985065945518 |
Real period |
R |
7.8062613431482 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001503 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
75712cd1 37856s1 448d1 |
Quadratic twists by: -4 8 13 |