Atkin-Lehner |
2+ 3+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
7968c |
Isogeny class |
Conductor |
7968 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
21760 |
Modular degree for the optimal curve |
Δ |
-82612224 = -1 · 212 · 35 · 83 |
Discriminant |
Eigenvalues |
2+ 3+ 3 -2 3 -4 -4 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-145729,-21363983] |
[a1,a2,a3,a4,a6] |
j |
-83561205858628672/20169 |
j-invariant |
L |
1.954802100985 |
L(r)(E,1)/r! |
Ω |
0.12217513131156 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7968h1 15936k1 23904s1 |
Quadratic twists by: -4 8 -3 |