Atkin-Lehner |
2+ 5- 7- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69440bx |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
568852480 = 219 · 5 · 7 · 31 |
Discriminant |
Eigenvalues |
2+ -1 5- 7- -3 -5 -6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-37665,2826145] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:2008:1] [57:928:1] |
Generators of the group modulo torsion |
j |
22542871522249/2170 |
j-invariant |
L |
9.0945649568617 |
L(r)(E,1)/r! |
Ω |
1.257963569108 |
Real period |
R |
1.8073983182484 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999646 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69440dd1 2170c1 |
Quadratic twists by: -4 8 |