Atkin-Lehner |
2- 3- 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48048cw |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
-82173068044075008 = -1 · 216 · 32 · 78 · 11 · 133 |
Discriminant |
Eigenvalues |
2- 3- 0 7- 11- 13+ -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-145608,25398900] |
[a1,a2,a3,a4,a6] |
Generators |
[222:2016:1] |
Generators of the group modulo torsion |
j |
-83353234419015625/20061784190448 |
j-invariant |
L |
7.5572254693093 |
L(r)(E,1)/r! |
Ω |
0.32604065897409 |
Real period |
R |
1.4486738964295 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000029 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6006a1 |
Quadratic twists by: -4 |