Atkin-Lehner |
2+ 3- 61- |
Signs for the Atkin-Lehner involutions |
Class |
8784b |
Isogeny class |
Conductor |
8784 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
21504 |
Modular degree for the optimal curve |
Δ |
-217798500824064 = -1 · 210 · 320 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -1 3 -5 -1 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,14757,167546] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:306:1] |
Generators of the group modulo torsion |
j |
476091534236/291761109 |
j-invariant |
L |
4.2034111913113 |
L(r)(E,1)/r! |
Ω |
0.34566004739176 |
Real period |
R |
3.0401338128523 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4392d1 35136bs1 2928a1 |
Quadratic twists by: -4 8 -3 |