Atkin-Lehner |
2- 3+ 7- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
129948l |
Isogeny class |
Conductor |
129948 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
32746896 = 24 · 33 · 73 · 13 · 17 |
Discriminant |
Eigenvalues |
2- 3+ -1 7- 0 13+ 17- -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-86,-111] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:-7:1] [-5:13:1] |
Generators of the group modulo torsion |
j |
12967168/5967 |
j-invariant |
L |
10.164881758315 |
L(r)(E,1)/r! |
Ω |
1.6365424261015 |
Real period |
R |
1.0351989254834 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999923902 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129948bf1 |
Quadratic twists by: -7 |