Atkin-Lehner |
31- 89- |
Signs for the Atkin-Lehner involutions |
Class |
85529d |
Isogeny class |
Conductor |
85529 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
56580 |
Modular degree for the optimal curve |
Δ |
-78987827609 = -1 · 316 · 89 |
Discriminant |
Eigenvalues |
-1 1 -1 -4 2 -2 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-981,-18046] |
[a1,a2,a3,a4,a6] |
Generators |
[43:119:1] |
Generators of the group modulo torsion |
j |
-117649/89 |
j-invariant |
L |
1.7112813263437 |
L(r)(E,1)/r! |
Ω |
0.41297581836351 |
Real period |
R |
4.1437809516851 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999807303 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89a1 |
Quadratic twists by: -31 |