Atkin-Lehner |
2+ 3- 5+ 13- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030l |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
403200 |
Modular degree for the optimal curve |
Δ |
10779536175525000 = 23 · 39 · 55 · 135 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -1 3 13- 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-56025,1062661] |
[a1,a2,a3,a4,a6] |
Generators |
[-85:2324:1] |
Generators of the group modulo torsion |
j |
26677562117216401/14786743725000 |
j-invariant |
L |
4.5607726561727 |
L(r)(E,1)/r! |
Ω |
0.3512619380079 |
Real period |
R |
0.6491982424943 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999457 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23010n1 |
Quadratic twists by: -3 |