Atkin-Lehner |
2+ 3+ 23- 29- |
Signs for the Atkin-Lehner involutions |
Class |
128064r |
Isogeny class |
Conductor |
128064 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-3457728 = -1 · 26 · 34 · 23 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 4 -3 3 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,27,-81] |
[a1,a2,a3,a4,a6] |
Generators |
[10:33:1] |
Generators of the group modulo torsion |
j |
32768000/54027 |
j-invariant |
L |
6.7605814818537 |
L(r)(E,1)/r! |
Ω |
1.318709581276 |
Real period |
R |
2.5633321968329 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000003837 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128064da1 2001c1 |
Quadratic twists by: -4 8 |