Atkin-Lehner |
3- 5- 7+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
19215r |
Isogeny class |
Conductor |
19215 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
3283062890625 = 39 · 58 · 7 · 61 |
Discriminant |
Eigenvalues |
-1 3- 5- 7+ -4 -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-4037,47324] |
[a1,a2,a3,a4,a6] |
Generators |
[-68:96:1] [9:103:1] |
Generators of the group modulo torsion |
j |
9978645018889/4503515625 |
j-invariant |
L |
4.9389874221697 |
L(r)(E,1)/r! |
Ω |
0.71372073459414 |
Real period |
R |
3.4600279792758 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999994 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
6405j1 96075bk1 |
Quadratic twists by: -3 5 |