Atkin-Lehner |
3+ 5- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
129285j |
Isogeny class |
Conductor |
129285 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
19968 |
Modular degree for the optimal curve |
Δ |
-48481875 = -1 · 33 · 54 · 132 · 17 |
Discriminant |
Eigenvalues |
0 3+ 5- 0 -3 13+ 17- -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,78,-205] |
[a1,a2,a3,a4,a6] |
Generators |
[3:7:1] |
Generators of the group modulo torsion |
j |
11501568/10625 |
j-invariant |
L |
4.960796946688 |
L(r)(E,1)/r! |
Ω |
1.1004867225232 |
Real period |
R |
0.56347760205643 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999981192 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129285a1 129285f1 |
Quadratic twists by: -3 13 |