Atkin-Lehner |
2- 3+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
68952w |
Isogeny class |
Conductor |
68952 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
-665636268336 = -1 · 24 · 3 · 138 · 17 |
Discriminant |
Eigenvalues |
2- 3+ -2 2 -4 13+ 17- 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2141,8644] |
[a1,a2,a3,a4,a6] |
Generators |
[9:169:1] |
Generators of the group modulo torsion |
j |
14047232/8619 |
j-invariant |
L |
4.719069104455 |
L(r)(E,1)/r! |
Ω |
0.56022732038315 |
Real period |
R |
1.0529362217724 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
3.9999999999929 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5304c1 |
Quadratic twists by: 13 |