x^12 - x^9*y^3 + x^6*y^6 - x^3*y^9 + y^12 - 4*x^9*z^3 + 3*x^6*y^3*z^3 - 2*x^3*y^6*z^3 + y^9*z^3 + 6*x^6*z^6 - 3*x^3*y^3*z^6 + y^6*z^6 - 4*x^3*z^9 + y^3*z^9 + z^12

def tesgfppoints2():
   L1=5*10^4
   L2=2*L1
   for p in primes(L1,L2):
          K.<x,y,z>=GF(p)[]
          F=x^12 - x^9*y^3 + x^6*y^6 - x^3*y^9 + y^12 - 4*x^9*z^3 + 3*x^6*y^3*z^3 - 2*x^3*y^6*z^3 + y^9*z^3 + 6*x^6*z^6 - 3*x^3*y^3*z^6 + y^6*z^6 - 4*x^3*z^9 + y^3*z^9 + z^12
          C=Curve(F)
          ire=C.is_irreducible()
          if not ire:  continue
          rp=len(C.rational_points())

          print 'p=',p,';rp=',rp,'ir=',ire,'g=',C.genus()