Atkin-Lehner |
2- 3- 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48048cc |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
4681896604729344 = 232 · 32 · 7 · 113 · 13 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 11+ 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-368824,86028116] |
[a1,a2,a3,a4,a6] |
Generators |
[887:21390:1] |
Generators of the group modulo torsion |
j |
1354635530322645817/1143041163264 |
j-invariant |
L |
5.2664149284211 |
L(r)(E,1)/r! |
Ω |
0.43121180944859 |
Real period |
R |
6.1065291035772 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000025 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6006i1 |
Quadratic twists by: -4 |