Atkin-Lehner |
13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
15041a |
Isogeny class |
Conductor |
15041 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
429586001 = 136 · 89 |
Discriminant |
Eigenvalues |
-1 2 2 -2 4 13+ 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-257,1126] |
[a1,a2,a3,a4,a6] |
Generators |
[-1580:7038:125] |
Generators of the group modulo torsion |
j |
389017/89 |
j-invariant |
L |
5.0389381416246 |
L(r)(E,1)/r! |
Ω |
1.5779055357287 |
Real period |
R |
6.3868692105164 |
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 |
89b2 |
Quadratic twists by: 13 |