Atkin-Lehner |
2- 3+ 13- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
19032n |
Isogeny class |
Conductor |
19032 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
147992832 = 28 · 36 · 13 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 0 0 0 13- 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-228,-1116] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:8:1] |
Generators of the group modulo torsion |
j |
5142706000/578097 |
j-invariant |
L |
4.2707717095575 |
L(r)(E,1)/r! |
Ω |
1.2371444485482 |
Real period |
R |
1.7260602488939 |
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 |
38064l1 57096g1 |
Quadratic twists by: -4 -3 |