Atkin-Lehner |
2- 3- 5+ 13+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
47970be |
Isogeny class |
Conductor |
47970 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
80640 |
Modular degree for the optimal curve |
Δ |
-87285444480 = -1 · 27 · 39 · 5 · 132 · 41 |
Discriminant |
Eigenvalues |
2- 3- 5+ -5 -2 13+ -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-608,15491] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:121:1] [-23:141:1] |
Generators of the group modulo torsion |
j |
-34043726521/119733120 |
j-invariant |
L |
11.446685097384 |
L(r)(E,1)/r! |
Ω |
0.94220311905484 |
Real period |
R |
0.21694376391979 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15990k1 |
Quadratic twists by: -3 |