Atkin-Lehner |
2+ 43+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
129344i |
Isogeny class |
Conductor |
129344 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
22272 |
Modular degree for the optimal curve |
Δ |
2069504 = 210 · 43 · 47 |
Discriminant |
Eigenvalues |
2+ 0 1 -4 6 -6 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-32,8] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:8:1] [14:48:1] |
Generators of the group modulo torsion |
j |
3538944/2021 |
j-invariant |
L |
11.305850708298 |
L(r)(E,1)/r! |
Ω |
2.2404639883065 |
Real period |
R |
2.5231047586855 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000635 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129344z1 8084c1 |
Quadratic twists by: -4 8 |