Atkin-Lehner |
2- 3- 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
36192z |
Isogeny class |
Conductor |
36192 |
Conductor |
∏ cp |
19 |
Product of Tamagawa factors cp |
deg |
128896 |
Modular degree for the optimal curve |
Δ |
-224344357406208 = -1 · 29 · 319 · 13 · 29 |
Discriminant |
Eigenvalues |
2- 3- 0 -4 5 13+ -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-12288,-895284] |
[a1,a2,a3,a4,a6] |
Generators |
[339:5832:1] |
Generators of the group modulo torsion |
j |
-400804604117000/438172573059 |
j-invariant |
L |
6.2318068473734 |
L(r)(E,1)/r! |
Ω |
0.21737754742957 |
Real period |
R |
1.5088487194316 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
36192u1 72384cn1 108576j1 |
Quadratic twists by: -4 8 -3 |