Atkin-Lehner |
5+ 23- 71- |
Signs for the Atkin-Lehner involutions |
Class |
8165a |
Isogeny class |
Conductor |
8165 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
712 |
Modular degree for the optimal curve |
Δ |
8165 = 5 · 23 · 71 |
Discriminant |
Eigenvalues |
0 -2 5+ -2 -3 -6 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-21,-45] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:0:1] |
Generators of the group modulo torsion |
j |
1073741824/8165 |
j-invariant |
L |
1.1550973341969 |
L(r)(E,1)/r! |
Ω |
2.2224601604881 |
Real period |
R |
0.51973815087115 |
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 |
73485i1 40825a1 |
Quadratic twists by: -3 5 |