Atkin-Lehner |
2- 3- 7- 23+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
84042br |
Isogeny class |
Conductor |
84042 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
2785915653696 = 26 · 38 · 73 · 23 · 292 |
Discriminant |
Eigenvalues |
2- 3- 2 7- -4 4 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-14009,-629607] |
[a1,a2,a3,a4,a6] |
Generators |
[-69:104:1] |
Generators of the group modulo torsion |
j |
417050384385097/3821557824 |
j-invariant |
L |
12.57309966929 |
L(r)(E,1)/r! |
Ω |
0.43907667247723 |
Real period |
R |
1.5908509397366 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002233 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28014e1 |
Quadratic twists by: -3 |