Atkin-Lehner |
5- 23+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
8165c |
Isogeny class |
Conductor |
8165 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
736 |
Modular degree for the optimal curve |
Δ |
-2898575 = -1 · 52 · 23 · 712 |
Discriminant |
Eigenvalues |
-1 0 5- 0 0 2 0 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-12,86] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:9:1] |
Generators of the group modulo torsion |
j |
-176558481/2898575 |
j-invariant |
L |
2.7610365426454 |
L(r)(E,1)/r! |
Ω |
2.1454235988834 |
Real period |
R |
1.2869423754276 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
73485e1 40825d1 |
Quadratic twists by: -3 5 |