Atkin-Lehner |
2- 3+ 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48048bu |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-2717895892647936 = -1 · 214 · 3 · 74 · 116 · 13 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 11- 13+ -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,17016,2352624] |
[a1,a2,a3,a4,a6] |
Generators |
[29:-1694:1] [-70:902:1] |
Generators of the group modulo torsion |
j |
133018079080823/663548801916 |
j-invariant |
L |
7.691661929587 |
L(r)(E,1)/r! |
Ω |
0.3266971099269 |
Real period |
R |
0.98098790590627 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6006j1 |
Quadratic twists by: -4 |