Atkin-Lehner |
2+ 3- 7- 23- 29- |
Signs for the Atkin-Lehner involutions |
Class |
84042z |
Isogeny class |
Conductor |
84042 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
215040 |
Modular degree for the optimal curve |
Δ |
-55604234631204 = -1 · 22 · 311 · 76 · 23 · 29 |
Discriminant |
Eigenvalues |
2+ 3- -1 7- -1 -5 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-9450,-501368] |
[a1,a2,a3,a4,a6] |
Generators |
[266:-4102:1] |
Generators of the group modulo torsion |
j |
-128031684631201/76274670276 |
j-invariant |
L |
4.2383458663979 |
L(r)(E,1)/r! |
Ω |
0.23567871014739 |
Real period |
R |
0.37465782135893 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000014963 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28014q1 |
Quadratic twists by: -3 |