Atkin-Lehner |
2- 3+ 11+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
86592bt |
Isogeny class |
Conductor |
86592 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
7182286848 = 216 · 35 · 11 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 0 -4 11+ 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-146113,21545953] |
[a1,a2,a3,a4,a6] |
Generators |
[-291:6272:1] [219:52:1] |
Generators of the group modulo torsion |
j |
5263969051106500/109593 |
j-invariant |
L |
8.3009750015842 |
L(r)(E,1)/r! |
Ω |
0.95586464516714 |
Real period |
R |
8.68425780116 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999259 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
86592bj1 21648j1 |
Quadratic twists by: -4 8 |