Atkin-Lehner |
3- 31- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
11997a |
Isogeny class |
Conductor |
11997 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
-813360609 = -1 · 39 · 312 · 43 |
Discriminant |
Eigenvalues |
1 3- 3 -1 -3 1 2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-18,1377] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:35:1] |
Generators of the group modulo torsion |
j |
-912673/1115721 |
j-invariant |
L |
6.2681569067707 |
L(r)(E,1)/r! |
Ω |
1.2809467229728 |
Real period |
R |
1.2233445767799 |
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 |
3999a1 |
Quadratic twists by: -3 |