Atkin-Lehner |
2+ 5+ 29- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
68150d |
Isogeny class |
Conductor |
68150 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
120960 |
Modular degree for the optimal curve |
Δ |
-340750000000 = -1 · 27 · 59 · 29 · 47 |
Discriminant |
Eigenvalues |
2+ 0 5+ 4 6 4 3 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1292,33616] |
[a1,a2,a3,a4,a6] |
j |
-15271450641/21808000 |
j-invariant |
L |
3.458246541005 |
L(r)(E,1)/r! |
Ω |
0.86456163076989 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13630k1 |
Quadratic twists by: 5 |