Atkin-Lehner |
2- 3- 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48048cj |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
55296 |
Modular degree for the optimal curve |
Δ |
147345149952 = 212 · 33 · 7 · 114 · 13 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 11- 13+ -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1464,-11628] |
[a1,a2,a3,a4,a6] |
Generators |
[54:264:1] [-9:30:1] |
Generators of the group modulo torsion |
j |
84778086457/35972937 |
j-invariant |
L |
9.9503746278847 |
L(r)(E,1)/r! |
Ω |
0.80171424474448 |
Real period |
R |
1.0342810934105 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3003e1 |
Quadratic twists by: -4 |