Atkin-Lehner |
2+ 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
89232w |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-7349861376 = -1 · 210 · 33 · 112 · 133 |
Discriminant |
Eigenvalues |
2+ 3- -2 -2 11- 13- -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-264,4356] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:60:1] [-9:78:1] |
Generators of the group modulo torsion |
j |
-907924/3267 |
j-invariant |
L |
11.351568783135 |
L(r)(E,1)/r! |
Ω |
1.1572310715802 |
Real period |
R |
0.81743749240975 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999996837 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
44616n1 89232o1 |
Quadratic twists by: -4 13 |