Atkin-Lehner |
2+ 3+ 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112a |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
435456 |
Modular degree for the optimal curve |
Δ |
-31931101268543664 = -1 · 24 · 39 · 119 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ -1 1 11+ -6 -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-32778,-8895609] |
[a1,a2,a3,a4,a6] |
j |
-12366869833728/101391750713 |
j-invariant |
L |
0.31219499726077 |
L(r)(E,1)/r! |
Ω |
0.15609749557865 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34056a1 68112b1 |
Quadratic twists by: -4 -3 |