Atkin-Lehner |
2- 3- 5- 13- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030bo |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
149760 |
Modular degree for the optimal curve |
Δ |
8408347702560 = 25 · 39 · 5 · 13 · 593 |
Discriminant |
Eigenvalues |
2- 3- 5- -1 3 13- -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-9302,-313531] |
[a1,a2,a3,a4,a6] |
Generators |
[-51:187:1] |
Generators of the group modulo torsion |
j |
122090372373529/11534084640 |
j-invariant |
L |
11.019819836575 |
L(r)(E,1)/r! |
Ω |
0.48908334744453 |
Real period |
R |
2.2531578499221 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000877 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23010f1 |
Quadratic twists by: -3 |