Atkin-Lehner |
2- 11+ 13- 37- |
Signs for the Atkin-Lehner involutions |
Class |
84656p |
Isogeny class |
Conductor |
84656 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-12419232956416 = -1 · 219 · 113 · 13 · 372 |
Discriminant |
Eigenvalues |
2- 0 -3 -3 11+ 13- 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-27179,1732954] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:1406:1] [85:192:1] |
Generators of the group modulo torsion |
j |
-542080999521153/3032039296 |
j-invariant |
L |
7.7007488393866 |
L(r)(E,1)/r! |
Ω |
0.71570261713836 |
Real period |
R |
1.3449630919812 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000393 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10582l1 |
Quadratic twists by: -4 |