Atkin-Lehner |
2- 3- 19- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
20862v |
Isogeny class |
Conductor |
20862 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
48384 |
Modular degree for the optimal curve |
Δ |
-4208278634496 = -1 · 218 · 36 · 192 · 61 |
Discriminant |
Eigenvalues |
2- 3- -3 -3 -1 -3 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1769,103209] |
[a1,a2,a3,a4,a6] |
Generators |
[-37:360:1] [-1:324:1] |
Generators of the group modulo torsion |
j |
-839362385737/5772673024 |
j-invariant |
L |
8.7105729455021 |
L(r)(E,1)/r! |
Ω |
0.67023135161733 |
Real period |
R |
0.18050510395658 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2318a1 |
Quadratic twists by: -3 |