Atkin-Lehner |
2- 3- 5+ 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030bg |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
18688 |
Modular degree for the optimal curve |
Δ |
16774290 = 2 · 37 · 5 · 13 · 59 |
Discriminant |
Eigenvalues |
2- 3- 5+ 3 3 13+ -2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-68,101] |
[a1,a2,a3,a4,a6] |
Generators |
[-66:83:8] |
Generators of the group modulo torsion |
j |
47045881/23010 |
j-invariant |
L |
11.031528438173 |
L(r)(E,1)/r! |
Ω |
1.9503818111302 |
Real period |
R |
2.8280433027164 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000689 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23010i1 |
Quadratic twists by: -3 |