Atkin-Lehner |
3- 11- 17- 53- |
Signs for the Atkin-Lehner involutions |
Class |
89199k |
Isogeny class |
Conductor |
89199 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
721728 |
Modular degree for the optimal curve |
Δ |
336284052979941 = 36 · 116 · 173 · 53 |
Discriminant |
Eigenvalues |
-2 3- 3 -4 11- 3 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-74691,-7807192] |
[a1,a2,a3,a4,a6] |
Generators |
[-167:93:1] |
Generators of the group modulo torsion |
j |
63212214608990208/461294997229 |
j-invariant |
L |
3.7051089993594 |
L(r)(E,1)/r! |
Ω |
0.28891728705004 |
Real period |
R |
0.71245092545655 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000001526 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9911b1 |
Quadratic twists by: -3 |