n = 3 : irreducible factors (u-values of nonzero n-torsion points), marking factors removed:
   deg  2 : u**2 - u + 1   | J-poly: t**2
   number of parameters |P^1[3]| = 2  (expected n^2/3 - 1 = 2 if 3|n)
   marking factors present: ['u - 1', 'u']
n = 6 : irreducible factors (u-values of nonzero n-torsion points), marking factors removed:
   deg  1 : u - 2   | J-poly: 27 - 4*t
   deg  1 : u + 1   | J-poly: 27 - 4*t
   deg  2 : u**2 - u + 1   | J-poly: t**2
   deg  6 : u**6 - 3*u**5 + 60*u**4 - 115*u**3 + 60*u**2 - 3*u + 1   | J-poly: (t + 54)**6
   deg  1 : u - 1/2   | J-poly: -(4*t - 27)/64
   number of parameters |P^1[6]| = 11  (expected n^2/3 - 1 = 11 if 3|n)
   marking factors present: ['u - 1', 'u']
n = 9 : irreducible factors (u-values of nonzero n-torsion points), marking factors removed:
   deg  2 : u**2 - u + 1   | J-poly: t**2
   deg  3 : u**3 - 6*u**2 + 3*u + 1   | J-poly: -(t - 27)**3
   deg  3 : u**3 + 3*u**2 - 6*u + 1   | J-poly: -(t - 27)**3
   deg 18 : u**18 - 9*u**17 + 693*u**16 - 5340*u**15 + 24633*u**14 - 79695*u**13 + 171087*u**12 - 230805*u**11 + 202167*u**10 - 165463*u**9 + 202167*u**8 - 230805*u**7 + 171087*u**6 - 79695*u**5 + 24633*u**4 - 5340*u**3 + 693*u**2 - 9*u + 1   | J-poly: (t**3 + 648*t**2 + 2187*t - 19683)**6
   number of parameters |P^1[9]| = 26  (expected n^2/3 - 1 = 26 if 3|n)
   marking factors present: ['u - 1', 'u']
printed P == (u^2-u-1)^3+2 : True
printed P == (u^2-u+1)^3 - 6u^2(u-1)^2 (i.e. J = 6 on its roots): True
claim Q expanded: u**6 - 3*u**5 + 60*u**4 - 115*u**3 + 60*u**2 - 3*u + 1
BHRS tau: resultant poly in u factors as u**6 - 3*u**5 + 60*u**4 - 115*u**3 + 60*u**2 - 3*u + 1
   ... Q_claim divides it: True ; printed P divides it: False
