Atkin-Lehner |
2- 3- 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112bu |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
67477048192401408 = 228 · 312 · 11 · 43 |
Discriminant |
Eigenvalues |
2- 3- 2 0 11+ -2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1046739,412008338] |
[a1,a2,a3,a4,a6] |
j |
42476766863084497/22597926912 |
j-invariant |
L |
2.7454780428274 |
L(r)(E,1)/r! |
Ω |
0.343184755159 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8514d1 22704bd1 |
Quadratic twists by: -4 -3 |