Atkin-Lehner |
2- 3- 5+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
51120bb |
Isogeny class |
Conductor |
51120 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
294912 |
Modular degree for the optimal curve |
Δ |
-4884592066560000 = -1 · 224 · 38 · 54 · 71 |
Discriminant |
Eigenvalues |
2- 3- 5+ 4 0 -2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-74883,8574082] |
[a1,a2,a3,a4,a6] |
Generators |
[-169:4050:1] |
Generators of the group modulo torsion |
j |
-15551989015681/1635840000 |
j-invariant |
L |
6.8198665602068 |
L(r)(E,1)/r! |
Ω |
0.42160419299884 |
Real period |
R |
2.0219991503366 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000045 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6390j1 17040bc1 |
Quadratic twists by: -4 -3 |