Atkin-Lehner |
89- |
Signs for the Atkin-Lehner involutions |
Class |
89b |
Isogeny class |
Conductor |
89 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
5 |
Modular degree for the optimal curve |
Δ |
-7921 = -1 · 892 |
Discriminant |
Eigenvalues |
1 2 -2 2 -4 2 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,4,5] |
[a1,a2,a3,a4,a6] |
j |
4657463/7921 |
j-invariant |
L |
1.4223048292271 |
L(r)(E,1)/r! |
Ω |
2.8446096584542 |
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 |
1424f2 5696g2 801b2 2225b2 |
Quadratic twists by: -4 8 -3 5 |