Atkin-Lehner |
2+ 3- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
89232p |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
41472 |
Modular degree for the optimal curve |
Δ |
3100722768 = 24 · 36 · 112 · 133 |
Discriminant |
Eigenvalues |
2+ 3- 2 -2 11+ 13- -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-407,1548] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:66:1] |
Generators of the group modulo torsion |
j |
212629504/88209 |
j-invariant |
L |
8.6379011083196 |
L(r)(E,1)/r! |
Ω |
1.2863863155602 |
Real period |
R |
1.1191429562921 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.00000000041 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
44616e1 89232v1 |
Quadratic twists by: -4 13 |