Atkin-Lehner |
2+ 3+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384j |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
614400 |
Modular degree for the optimal curve |
Δ |
2097890187973632 = 210 · 38 · 135 · 292 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -4 2 13+ 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-498189,-135160227] |
[a1,a2,a3,a4,a6] |
j |
13353866478112073728/2048720886693 |
j-invariant |
L |
0.35940570194968 |
L(r)(E,1)/r! |
Ω |
0.17970284244606 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384dc1 9048j1 |
Quadratic twists by: -4 8 |