Atkin-Lehner |
3- 17+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
8109d |
Isogeny class |
Conductor |
8109 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2112 |
Modular degree for the optimal curve |
Δ |
1970487 = 37 · 17 · 53 |
Discriminant |
Eigenvalues |
-1 3- -4 -3 -4 5 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-32,20] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:10:1] [-2:9:1] |
Generators of the group modulo torsion |
j |
4826809/2703 |
j-invariant |
L |
2.9371654621846 |
L(r)(E,1)/r! |
Ω |
2.2683759455895 |
Real period |
R |
0.32370796691513 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129744bg1 2703d1 |
Quadratic twists by: -4 -3 |