Atkin-Lehner |
2+ 3+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
48642f |
Isogeny class |
Conductor |
48642 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
12819015396 = 22 · 33 · 116 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -2 11- 0 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-4479,-117135] |
[a1,a2,a3,a4,a6] |
Generators |
[-40:25:1] [160:1735:1] |
Generators of the group modulo torsion |
j |
5611284433/7236 |
j-invariant |
L |
6.59789993669 |
L(r)(E,1)/r! |
Ω |
0.58361345316218 |
Real period |
R |
5.652628380087 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
402c1 |
Quadratic twists by: -11 |