Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
8712m |
Isogeny class |
Conductor |
8712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-90326016 = -1 · 210 · 36 · 112 |
Discriminant |
Eigenvalues |
2+ 3- -3 -4 11- -3 3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-99,-594] |
[a1,a2,a3,a4,a6] |
Generators |
[15:36:1] |
Generators of the group modulo torsion |
j |
-1188 |
j-invariant |
L |
2.701478822792 |
L(r)(E,1)/r! |
Ω |
0.73077581675038 |
Real period |
R |
0.92418179449513 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17424x1 69696df1 968d1 8712z1 |
Quadratic twists by: -4 8 -3 -11 |