Atkin-Lehner |
2- 3+ 13- 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384cm |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
675840 |
Modular degree for the optimal curve |
Δ |
2420199791612928 = 210 · 32 · 135 · 294 |
Discriminant |
Eigenvalues |
2- 3+ 0 -4 2 13- -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-491693,132848493] |
[a1,a2,a3,a4,a6] |
Generators |
[-83:13156:1] [372:1131:1] |
Generators of the group modulo torsion |
j |
12838276213282048000/2363476358997 |
j-invariant |
L |
8.2812400681977 |
L(r)(E,1)/r! |
Ω |
0.44498716439164 |
Real period |
R |
0.93050325165659 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999521 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384bj1 18096k1 |
Quadratic twists by: -4 8 |