Atkin-Lehner |
2- 5+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
68770m |
Isogeny class |
Conductor |
68770 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1689600 |
Modular degree for the optimal curve |
Δ |
101135028375437680 = 24 · 5 · 135 · 237 |
Discriminant |
Eigenvalues |
2- 3 5+ -3 2 13+ -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-339453,-74484779] |
[a1,a2,a3,a4,a6] |
Generators |
[-46817337:172463740:132651] |
Generators of the group modulo torsion |
j |
29220958012401/683179120 |
j-invariant |
L |
15.61759789212 |
L(r)(E,1)/r! |
Ω |
0.19807204529724 |
Real period |
R |
9.8560083696116 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001431 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2990i1 |
Quadratic twists by: -23 |