Atkin-Lehner |
2- 3+ 5- 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
61710bz |
Isogeny class |
Conductor |
61710 |
Conductor |
∏ cp |
256 |
Product of Tamagawa factors cp |
deg |
2211840 |
Modular degree for the optimal curve |
Δ |
5908144473000330000 = 24 · 3 · 54 · 119 · 174 |
Discriminant |
Eigenvalues |
2- 3+ 5- 0 11- -2 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-6337680,6137309025] |
[a1,a2,a3,a4,a6] |
Generators |
[1503:2393:1] |
Generators of the group modulo torsion |
j |
15891267085572193561/3334993530000 |
j-invariant |
L |
8.5221760149642 |
L(r)(E,1)/r! |
Ω |
0.23286509906794 |
Real period |
R |
2.2873157164865 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.00000000003 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
5610i1 |
Quadratic twists by: -11 |