Atkin-Lehner |
2- 17+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
12784c |
Isogeny class |
Conductor |
12784 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
23040 |
Modular degree for the optimal curve |
Δ |
157508698112 = 222 · 17 · 472 |
Discriminant |
Eigenvalues |
2- -2 0 -4 2 6 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-12688,545556] |
[a1,a2,a3,a4,a6] |
Generators |
[84:282:1] |
Generators of the group modulo torsion |
j |
55154061924625/38454272 |
j-invariant |
L |
2.7039616194822 |
L(r)(E,1)/r! |
Ω |
1.0149152226943 |
Real period |
R |
1.3321120616873 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1598a1 51136i1 115056ba1 |
Quadratic twists by: -4 8 -3 |