Atkin-Lehner |
2- 3- 19- 47- |
Signs for the Atkin-Lehner involutions |
Class |
128592m |
Isogeny class |
Conductor |
128592 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
1367906144256 = 212 · 39 · 192 · 47 |
Discriminant |
Eigenvalues |
2- 3- -1 3 3 -2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5088,127856] |
[a1,a2,a3,a4,a6] |
Generators |
[-47:513:1] |
Generators of the group modulo torsion |
j |
4878401536/458109 |
j-invariant |
L |
8.1806286736312 |
L(r)(E,1)/r! |
Ω |
0.83256690400661 |
Real period |
R |
1.2282239286135 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999074039 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8037a1 42864b1 |
Quadratic twists by: -4 -3 |