Atkin-Lehner |
2+ 3+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384i |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
405504 |
Modular degree for the optimal curve |
Δ |
104492614726656 = 210 · 36 · 136 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -4 6 13+ -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-31117,-2044355] |
[a1,a2,a3,a4,a6] |
j |
3254099827320832/102043569069 |
j-invariant |
L |
0.72029898024333 |
L(r)(E,1)/r! |
Ω |
0.36014949639214 |
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 |
72384cz1 9048n1 |
Quadratic twists by: -4 8 |