Atkin-Lehner |
3- 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
10413g |
Isogeny class |
Conductor |
10413 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
48960 |
Modular degree for the optimal curve |
Δ |
-12102628655871 = -1 · 321 · 13 · 89 |
Discriminant |
Eigenvalues |
1 3- -3 1 3 13+ 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-515511,142593016] |
[a1,a2,a3,a4,a6] |
Generators |
[452:1106:1] |
Generators of the group modulo torsion |
j |
-20783106726980601457/16601685399 |
j-invariant |
L |
4.3590004611855 |
L(r)(E,1)/r! |
Ω |
0.59401948325991 |
Real period |
R |
3.6690719614648 |
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 |
3471a1 |
Quadratic twists by: -3 |