Atkin-Lehner |
3- 11- 17+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
89199g |
Isogeny class |
Conductor |
89199 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
117504 |
Modular degree for the optimal curve |
Δ |
-1163612640069 = -1 · 36 · 116 · 17 · 53 |
Discriminant |
Eigenvalues |
-1 3- 3 -1 11- 5 17+ 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,2569,12804] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:51:1] |
Generators of the group modulo torsion |
j |
2573042579927/1596176461 |
j-invariant |
L |
5.476019826311 |
L(r)(E,1)/r! |
Ω |
0.53630365718604 |
Real period |
R |
0.85088919129134 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000008246 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9911c1 |
Quadratic twists by: -3 |