Atkin-Lehner |
2+ 3- 19- 89- |
Signs for the Atkin-Lehner involutions |
Class |
40584k |
Isogeny class |
Conductor |
40584 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-7120300464 = -1 · 24 · 36 · 193 · 89 |
Discriminant |
Eigenvalues |
2+ 3- -1 -4 -3 -5 -1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-111,-4122] |
[a1,a2,a3,a4,a6] |
Generators |
[18:6:1] [21:57:1] |
Generators of the group modulo torsion |
j |
-9538484224/445018779 |
j-invariant |
L |
8.9368870322809 |
L(r)(E,1)/r! |
Ω |
0.58075951726436 |
Real period |
R |
0.42745207719915 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81168g1 121752bf1 |
Quadratic twists by: -4 -3 |