Atkin-Lehner |
2- 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696gk |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
178754705852203008 = 222 · 37 · 117 |
Discriminant |
Eigenvalues |
2- 3- 2 -4 11- -6 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-140844,-362032] |
[a1,a2,a3,a4,a6] |
Generators |
[-371:909:1] [-176:4356:1] |
Generators of the group modulo torsion |
j |
912673/528 |
j-invariant |
L |
10.596407899359 |
L(r)(E,1)/r! |
Ω |
0.27007008112214 |
Real period |
R |
2.4522356973429 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999683 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696cm1 17424bz1 23232de1 6336ci1 |
Quadratic twists by: -4 8 -3 -11 |