Atkin-Lehner |
2- 7+ 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
68432f |
Isogeny class |
Conductor |
68432 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-227741696 = -1 · 212 · 7 · 132 · 47 |
Discriminant |
Eigenvalues |
2- -1 -3 7+ 1 13+ 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-112,896] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:26:1] [2:-26:1] |
Generators of the group modulo torsion |
j |
-38272753/55601 |
j-invariant |
L |
6.9854597941598 |
L(r)(E,1)/r! |
Ω |
1.5890495569495 |
Real period |
R |
1.0989996761914 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4277b1 |
Quadratic twists by: -4 |