Atkin-Lehner |
3- 5+ 7+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
8715i |
Isogeny class |
Conductor |
8715 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2048 |
Modular degree for the optimal curve |
Δ |
7625625 = 3 · 54 · 72 · 83 |
Discriminant |
Eigenvalues |
1 3- 5+ 7+ 2 -4 -4 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-64,137] |
[a1,a2,a3,a4,a6] |
Generators |
[54:11:8] |
Generators of the group modulo torsion |
j |
28344726649/7625625 |
j-invariant |
L |
5.5188404555261 |
L(r)(E,1)/r! |
Ω |
2.189191040308 |
Real period |
R |
2.5209496813717 |
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 |
26145l1 43575d1 61005g1 |
Quadratic twists by: -3 5 -7 |