Atkin-Lehner |
2- 3+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384bw |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
22528 |
Modular degree for the optimal curve |
Δ |
159027648 = 26 · 3 · 134 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 2 4 0 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-172,682] |
[a1,a2,a3,a4,a6] |
Generators |
[70290:575267:1000] |
Generators of the group modulo torsion |
j |
8844058432/2484807 |
j-invariant |
L |
7.5464026858951 |
L(r)(E,1)/r! |
Ω |
1.6953958596238 |
Real period |
R |
8.9022308763925 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001682 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384da1 36192s3 |
Quadratic twists by: -4 8 |