Atkin-Lehner |
13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
1157b |
Isogeny class |
Conductor |
1157 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
-2541929 = -1 · 134 · 89 |
Discriminant |
Eigenvalues |
-1 1 3 -4 2 13+ -5 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,6,77] |
[a1,a2,a3,a4,a6] |
Generators |
[19:75:1] |
Generators of the group modulo torsion |
j |
23639903/2541929 |
j-invariant |
L |
2.0835319816636 |
L(r)(E,1)/r! |
Ω |
1.9715172450819 |
Real period |
R |
0.52840825685422 |
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 |
18512e1 74048g1 10413h1 28925c1 |
Quadratic twists by: -4 8 -3 5 |