Atkin-Lehner |
2- 3+ 23- 29- |
Signs for the Atkin-Lehner involutions |
Class |
128064cs |
Isogeny class |
Conductor |
128064 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
-122215692091392 = -1 · 214 · 36 · 233 · 292 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 -6 2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,12047,-158639] |
[a1,a2,a3,a4,a6] |
Generators |
[40:621:1] [63:920:1] |
Generators of the group modulo torsion |
j |
11800609886000/7459453863 |
j-invariant |
L |
9.5119319673671 |
L(r)(E,1)/r! |
Ω |
0.33803764456586 |
Real period |
R |
2.3448897181736 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002302 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128064bc1 32016g1 |
Quadratic twists by: -4 8 |