Atkin-Lehner |
2- 3- 31+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69936u |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
152064 |
Modular degree for the optimal curve |
Δ |
-25372574908416 = -1 · 215 · 312 · 31 · 47 |
Discriminant |
Eigenvalues |
2- 3- 1 0 1 6 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2000,244116] |
[a1,a2,a3,a4,a6] |
Generators |
[4:-486:1] |
Generators of the group modulo torsion |
j |
-216108018001/6194476296 |
j-invariant |
L |
9.3278177748136 |
L(r)(E,1)/r! |
Ω |
0.56066164748876 |
Real period |
R |
0.69321501777008 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000608 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8742h1 |
Quadratic twists by: -4 |