Atkin-Lehner |
2+ 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
89232v |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
539136 |
Modular degree for the optimal curve |
Δ |
14966596563087312 = 24 · 36 · 112 · 139 |
Discriminant |
Eigenvalues |
2+ 3- -2 2 11- 13- -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-68839,3676232] |
[a1,a2,a3,a4,a6] |
j |
212629504/88209 |
j-invariant |
L |
2.1406761548324 |
L(r)(E,1)/r! |
Ω |
0.35677937083135 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
44616o1 89232p1 |
Quadratic twists by: -4 13 |