Atkin-Lehner |
2+ 3- 5- 47- |
Signs for the Atkin-Lehner involutions |
Class |
67680n |
Isogeny class |
Conductor |
67680 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
52224 |
Modular degree for the optimal curve |
Δ |
102789000000 = 26 · 37 · 56 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 -4 -4 -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1317,-10024] |
[a1,a2,a3,a4,a6] |
Generators |
[67:-450:1] [-13:70:1] |
Generators of the group modulo torsion |
j |
5414689216/2203125 |
j-invariant |
L |
10.68371098782 |
L(r)(E,1)/r! |
Ω |
0.8211745179985 |
Real period |
R |
1.0841900588425 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999582 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
67680h1 22560j1 |
Quadratic twists by: -4 -3 |