Atkin-Lehner |
2- 3+ 19- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
81168bx |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
225792 |
Modular degree for the optimal curve |
Δ |
-248183141695488 = -1 · 226 · 37 · 19 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 0 3 -3 -5 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1408,-757760] |
[a1,a2,a3,a4,a6] |
Generators |
[674466:11552234:2197] |
Generators of the group modulo torsion |
j |
-75418890625/60591587328 |
j-invariant |
L |
5.1705035155033 |
L(r)(E,1)/r! |
Ω |
0.24992739863211 |
Real period |
R |
10.344010978785 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000009291 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10146l1 |
Quadratic twists by: -4 |