Atkin-Lehner |
2- 3- 7- 17- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
42126z |
Isogeny class |
Conductor |
42126 |
Conductor |
∏ cp |
264 |
Product of Tamagawa factors cp |
deg |
861696 |
Modular degree for the optimal curve |
Δ |
-8659709592609266856 = -1 · 23 · 322 · 7 · 174 · 59 |
Discriminant |
Eigenvalues |
2- 3- 1 7- 0 2 17- -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-464065,-186724111] |
[a1,a2,a3,a4,a6] |
Generators |
[1160:28337:1] |
Generators of the group modulo torsion |
j |
-11052492159605261596561/8659709592609266856 |
j-invariant |
L |
12.666860247678 |
L(r)(E,1)/r! |
Ω |
0.088476629721985 |
Real period |
R |
0.54229610002073 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999985 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
126378s1 |
Quadratic twists by: -3 |