Atkin-Lehner |
3+ 5+ 13+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
13065d |
Isogeny class |
Conductor |
13065 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12960 |
Modular degree for the optimal curve |
Δ |
-3698374875 = -1 · 3 · 53 · 133 · 672 |
Discriminant |
Eigenvalues |
-2 3+ 5+ 3 3 13+ -1 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,174,2732] |
[a1,a2,a3,a4,a6] |
Generators |
[-7:33:1] |
Generators of the group modulo torsion |
j |
579259437056/3698374875 |
j-invariant |
L |
1.99660663936 |
L(r)(E,1)/r! |
Ω |
1.0153892883797 |
Real period |
R |
0.98317298705503 |
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 |
39195s1 65325y1 |
Quadratic twists by: -3 5 |