Atkin-Lehner |
2+ 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232k |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
903168 |
Modular degree for the optimal curve |
Δ |
64560052630122192 = 24 · 312 · 112 · 137 |
Discriminant |
Eigenvalues |
2+ 3+ -2 4 11- 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-129679,-13133810] |
[a1,a2,a3,a4,a6] |
j |
3122884507648/835956693 |
j-invariant |
L |
1.0264512933711 |
L(r)(E,1)/r! |
Ω |
0.25661282297477 |
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 |
44616s1 6864d1 |
Quadratic twists by: -4 13 |