Atkin-Lehner |
2- 23+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
42688p |
Isogeny class |
Conductor |
42688 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
638976 |
Modular degree for the optimal curve |
Δ |
-288101089918582784 = -1 · 226 · 236 · 29 |
Discriminant |
Eigenvalues |
2- 1 3 4 -3 -5 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,147871,13756703] |
[a1,a2,a3,a4,a6] |
Generators |
[-8645:223744:125] |
Generators of the group modulo torsion |
j |
1364048721284327/1099018439936 |
j-invariant |
L |
9.2006632013768 |
L(r)(E,1)/r! |
Ω |
0.19861509774831 |
Real period |
R |
5.7905109591926 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999947 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42688k1 10672d1 |
Quadratic twists by: -4 8 |