Atkin-Lehner |
2- 3- 7- 11+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
85008cg |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
50139758592 = 220 · 33 · 7 · 11 · 23 |
Discriminant |
Eigenvalues |
2- 3- -2 7- 11+ -6 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-16024,-786028] |
[a1,a2,a3,a4,a6] |
Generators |
[-73:6:1] [151:510:1] |
Generators of the group modulo torsion |
j |
111097343765017/12241152 |
j-invariant |
L |
11.827957356713 |
L(r)(E,1)/r! |
Ω |
0.42433361128138 |
Real period |
R |
9.2913979647469 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10626a1 |
Quadratic twists by: -4 |