  [ok] F2 at l = 0: graded datum has H = (1,3,6,5,3,2,1), dim D_4 = 3
  [ok] F2 at l = 1: graded datum has H = (1,3,6,5,3,2,1), dim D_4 = 3
  [ok] F2 at l = -2: graded datum has H = (1,3,6,5,3,2,1), dim D_4 = 3
  [ok] F2 at l = 17/5: graded datum has H = (1,3,6,5,3,2,1), dim D_4 = 3
  [info] (F2 family) l = 17/5: best S6.2/QT value found 40
  [info] (F2 family) l = -2: best S6.2/QT value found 40
  [info] (F2 family) l = 1: best S6.2/QT value found 40
  [ok] (F2 orbit) G = X^3*Y^2 + Y^5 + X^4*Z: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [2*x^7 + 3*x^6*y - x^5*y^2 - x^4*y^3 - 3*x^3*y^4 + 2*x^2*y^5 + x*y^6 + y^7 - 3*x^6*z + 3*x^5*y*z - x^4*y^2*z + 3*x^3*y^3*z - 2*x^2*y^4*z - 3*x*y^5*z + x^5*z^2 - 3*x^4*y*z^2 + 2*x^3*y^2*z^2 - 2*x^2*y^3*z^2 - 2*x*y^4*z^2 - 3*y^5*z^2 + 2*x^4*z^3 - 2*x^2*y^2*z^3 - 2*x*y^3*z^3 - 3*x^3*z^4 + 3*x^2*y*z^4 - x*y^2*z^4 - y^3*z^4 + 2*x^2*z^5 + y^2*z^5 - 3*x*z^6 - 3*y*z^6 + 2*z^7 + 1/24*x^6 + x^5*y + 2*x^4*y^2 - 3*x^3*y^3 - 2*x^2*y^4 + 2*x^5*z - x^4*y*z + 2*x^3*y^2*z + 2*x^2*y^3*z - 3*x*y^4*z - 3*y^5*z + 3*x^4*z^2 + 3*x^3*y*z^2 - 3*x^2*y^2*z^2 + x*y^3*z^2 - 2*x^3*z^3 - 2*x*y^2*z^3 - 2*y^3*z^3 - x^2*z^4 - x*y*z^4 - 2*x*z^5 - 2*z^6 + 2*x^4*y + 34*x^3*y^2 - 3*x^2*y^3 - 3*y^5 - 2*x^4*z - x^3*y*z - 3*x*y^3*z - y^4*z - 2*x^3*z^2 + x^2*y*z^2 - 2*x*y^2*z^2 + 2*y^3*z^2 + 3*x^2*z^3 + 2*x*y*z^3 - 3*y^2*z^3 + 3*x*z^4 + y*z^4 - 3*z^5 + 30*x^3*y - 6*x^2*y^2 + 3*x*y^3 - 3*y^4 + 3*x^3*z - 2*x*y^2*z + 2*y^3*z - 2*x^2*z^2 - x*y*z^2 + 2*y*z^3 + 2*z^4 + x*y*z + 3*y^2*z + 3*x*z^2 - y*z^2 + 2*z^3, -3*x^7 + 3*x^6*y + x^5*y^2 - x^4*y^3 - 3*x^3*y^4 - 2*x^2*y^5 + 2*x*y^6 + 2*y^7 + x^6*z + 2*x^5*y*z - 3*x^4*y^2*z - 2*x^3*y^3*z - 2*x^2*y^4*z - 3*y^6*z - 2*x^5*z^2 + 2*x^4*y*z^2 + 3*x^2*y^3*z^2 + 3*x*y^4*z^2 + y^5*z^2 - 3*x^4*z^3 - x^3*y*z^3 - 2*x^2*y^2*z^3 - x*y^3*z^3 - 2*x^2*y*z^4 - 3*x*y^2*z^4 - 2*y^3*z^4 - x^2*z^5 - x*y*z^5 + y^2*z^5 - 2*x*z^6 - y*z^6 - z^7 - 11/360*x^6 - 3*x^4*y^2 + 3*x^3*y^3 + 2*x^2*y^4 - 3*x*y^5 - y^6 + 2*x^5*z + 3*x^3*y^2*z - 3*x*y^4*z + 2*x^4*z^2 + x^3*y*z^2 - 3*x^2*y^2*z^2 + x*y^3*z^2 + y^4*z^2 - x^2*y*z^3 + y^3*z^3 - x^2*z^4 + x*y*z^4 - y^2*z^4 + 3*x*z^5 - 2*y*z^5 + z^6 - x^4*y - 30*x^3*y^2 - 2*x^2*y^3 - 3*x*y^4 + 3*y^5 - 2*x^3*y*z - x*y^3*z - 3*y^4*z + 3*x^3*z^2 - 2*x^2*y*z^2 + x*y^2*z^2 + 2*x^2*z^3 + 3*x*y*z^3 - 3*y^2*z^3 + 2*x*z^4 - 3*y*z^4 - 30*x^3*y - 4*x^2*y^2 + 3*y^4 + 2*x^3*z - 3*x^2*y*z + x*y^2*z - 3*y^3*z - 3*x^2*z^2 - x*y*z^2 + 3*y^2*z^2 - 2*x*z^3 - y*z^3 + 3*y^2*z - x*z^2 + y*z^2 - z^3, 3*x^7 - 3*x^6*y - 2*x^5*y^2 + x^4*y^3 - 3*x^3*y^4 + 2*x^2*y^5 - 3*x*y^6 + 2*y^7 - x^6*z - 2*x^5*y*z - 3*x^4*y^2*z + x^3*y^3*z - x^2*y^4*z + 3*x^5*z^2 + 2*x^4*y*z^2 - 2*x^3*y^2*z^2 - 2*x^2*y^3*z^2 - 2*x*y^4*z^2 - 2*y^5*z^2 - 2*x^4*z^3 - 3*x^3*y*z^3 + 3*x^2*y^2*z^3 + 3*x*y^3*z^3 + 2*y^4*z^3 - x^3*z^4 + 2*x^2*y*z^4 + 3*x*y^2*z^4 - 3*y^3*z^4 + x^2*z^5 + y^2*z^5 + 3*y*z^6 + 7/120*x^6 - x^5*y - 3*x^4*y^2 - 2*x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 - 3*y^6 + 3*x^5*z - 2*x^4*y*z - x^3*y^2*z - x^2*y^3*z - 2*x*y^4*z + y^5*z + 3*x^4*z^2 - 3*x^3*y*z^2 - 3*x^2*y^2*z^2 - x*y^3*z^2 + 3*y^4*z^2 + 2*x^3*z^3 + x^2*y*z^3 - 3*x*y^2*z^3 + y^3*z^3 - 2*x^2*z^4 + 2*x*y*z^4 + 2*y^2*z^4 - 3*x*z^5 + 3*z^6 + 3*x^4*y - 2*x^3*y^2 - 2*x^2*y^3 + x*y^4 + x^4*z + 2*x^3*y*z - 3*x^2*y^2*z + x*y^3*z - 2*y^4*z + 3*x^3*z^2 - 3*x^2*y*z^2 - x*y^2*z^2 - y^3*z^2 + 2*x^2*z^3 + 2*x*y*z^3 - y^2*z^3 - 2*x*z^4 - 2*z^5 + 20*x^3*y - 6*x^2*y^2 - 3*x*y^3 - 2*y^4 + 3*x^3*z + 2*x^2*y*z + 2*x*y^2*z + 2*y^3*z + x^2*z^2 + 2*x*y*z^2 - 3*y^2*z^2 + 3*x*z^3 - y*z^3 + z^4 - 2*x*y*z - 3*y^2*z - y*z^2 + 2*z^3]
  [ok] (F2 orbit) G = Y^5 + X^4*Z: QT(u=-x - 2*y + 3*z), triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-2*x^7 - 3*x^6*y + x^4*y^3 - 2*x^3*y^4 + 3*x^2*y^5 + 3*x*y^6 + 3*y^7 - 2*x^6*z - x^5*y*z + x^4*y^2*z - x^3*y^3*z - 2*x^2*y^4*z - 2*x*y^5*z - 2*y^6*z + 3*x^4*y*z^2 + 3*x^3*y^2*z^2 - 3*x*y^4*z^2 + y^5*z^2 - 2*x^3*y*z^3 - 2*x^2*y^2*z^3 + x*y^3*z^3 - 3*y^4*z^3 - 3*x^3*z^4 + x*y^2*z^4 + 2*y^3*z^4 - 2*x*y*z^5 + y^2*z^5 + x*z^6 - 3*y*z^6 - 1/30*x^6 + x^5*y - x^3*y^3 + 3*x^2*y^4 + 3*x*y^5 + y^6 + x^5*z - 2*x^4*y*z + 2*x^3*y^2*z + 3*x^2*y^3*z - 3*x*y^4*z + y^5*z - x^4*z^2 + x^3*y*z^2 + 2*x^2*y^2*z^2 - x*y^3*z^2 - 3*y^4*z^2 + 2*x^2*y*z^3 + 3*y^3*z^3 + 2*x^2*z^4 - 2*x*y*z^4 - 2*y^2*z^4 - 2*y*z^5 - z^6 + 1/90*x^5 + x^4*y - 2*x^3*y^2 - x^2*y^3 - x*y^4 + 13/18*y^5 - 2*x^4*z - 2*x^3*y*z - 2*x^2*y^2*z + x*y^3*z - 2*y^4*z + 3*x^3*z^2 + x^2*y*z^2 - 2*x*y^2*z^2 - 3*y^3*z^2 - 2*x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 - 2*y*z^4 + 2*z^5 - x^2*y^2 + 3*x^2*y*z + 2*x*y^2*z + 2*x^2*z^2 + x*y*z^2 + x*z^3 + 2*y*z^3 + 3*z^4 - 2*x*y*z + 3*y^2*z - x*z^2 + 2*y*z^2 + 2*z^3, 3*x^7 - 3*x^6*y - x^3*y^4 + x^2*y^5 - x*y^6 + y^7 + 2*x^6*z - x^5*y*z + 2*x^4*y^2*z + 2*x^3*y^3*z - x^2*y^4*z + 2*x*y^5*z - 2*y^6*z + x^4*y*z^2 + 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 - 2*x*y^4*z^2 - 2*y^5*z^2 - 3*x^4*z^3 + x^2*y^2*z^3 + 3*x*y^3*z^3 - y^4*z^3 + x^3*z^4 + x^2*y*z^4 - 3*x*y^2*z^4 - 3*y^3*z^4 - 2*x^2*z^5 - 3*x*y*z^5 + 2*y^2*z^5 + x*z^6 - 3*y*z^6 + z^7 - 29/720*x^6 - x^5*y + 2*x^3*y^3 - 3*x*y^5 - 3*y^6 - 3*x^5*z + 2*x^3*y^2*z - 2*x^2*y^3*z + x*y^4*z - y^5*z + x^4*z^2 + 3*x^3*y*z^2 + x^2*y^2*z^2 - 3*x*y^3*z^2 + 3*y^4*z^2 - 3*x^3*z^3 + x^2*y*z^3 + 2*x*y^2*z^3 - 2*x^2*z^4 + x*y*z^4 + 3*y^2*z^4 + 3*x*z^5 + 3*y*z^5 + 3*z^6 - 17/360*x^5 + 3*x^4*y - 3*x^3*y^2 - 2*x^2*y^3 - 493/360*y^5 - x^3*y*z - x*y^3*z + 2*y^4*z + 3*x^3*z^2 + 2*x*y^2*z^2 + 3*y^3*z^2 + 2*x^2*z^3 - 2*x*y*z^3 + 3*y^2*z^3 - 2*x*z^4 + 3*y*z^4 + 2*z^5 - x^3*y + 3*x^2*y^2 + 3*x*y^3 + x^2*y*z + 3*x*y^2*z + x*z^3 - 3*y*z^3 + 3*z^4 + x*y*z + 3*y^2*z + 3*x*z^2 - 3*y*z^2 + 2*z^3, 3*x^6*y + x^5*y^2 - 2*x^4*y^3 - x^3*y^4 + 3*x^2*y^5 + x*y^6 - 3*y^7 - 3*x^5*y*z - x^4*y^2*z + x^3*y^3*z + x*y^5*z + 3*y^6*z + 3*x^5*z^2 - x^4*y*z^2 - x^3*y^2*z^2 + 2*x^2*y^3*z^2 - 3*y^5*z^2 + 3*x^4*z^3 - 2*x^3*y*z^3 - x^2*y^2*z^3 - 3*y^4*z^3 - 2*x^3*z^4 - 3*x^2*y*z^4 - 3*x*y^2*z^4 + 3*y^3*z^4 + 3*x^2*z^5 + 2*x*y*z^5 + x*z^6 - y*z^6 + 2*z^7 + 1/144*x^6 + 2*x^5*y + 3*x^4*y^2 - 3*x^3*y^3 + x^2*y^4 - 2*x*y^5 - 3*y^6 + 2*x^5*z + 2*x^2*y^3*z - 2*x*y^4*z - 3*y^5*z - x^4*z^2 - x^3*y*z^2 - 3*x^2*y^2*z^2 - 2*x*y^3*z^2 - y^4*z^2 + 3*x^3*z^3 + 3*x^2*y*z^3 + 3*y^3*z^3 + 2*x^2*z^4 - 3*x*y*z^4 - 3*y^2*z^4 + 3*x*z^5 + 3*y*z^5 + z^6 - 1/360*x^5 + x^4*y + x^3*y^2 + x^2*y^3 + 2*x*y^4 - 173/360*y^5 + 2*x^4*z + x^3*y*z - 2*x*y^3*z - 2*x^3*z^2 - 3*x^2*y*z^2 + 2*y^3*z^2 - x^2*z^3 - x*y*z^3 + 3*y^2*z^3 + 3*x*z^4 - 2*y*z^4 + 3*z^5 + x^3*y + x^2*y^2 + x*y^3 - 3*x^2*y*z + x*y^2*z + 2*y^3*z + 3*x*y*z^2 - y^2*z^2 + y*z^3 + z^4 - x*y*z - 3*y*z^2]
  [ok] (F2 orbit) G = X^3*Y^2 + X*Y^4 + X^4*Z: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [3*x^7 - 3*x^6*y - 2*x^5*y^2 + 3*x^4*y^3 + x^3*y^4 + 2*x^2*y^5 + 2*x*y^6 - 2*y^7 + 3*x^5*y*z + 2*x^4*y^2*z - x^3*y^3*z + x^2*y^4*z + y^6*z + 3*x^5*z^2 + 3*x^4*y*z^2 - 3*x^3*y^2*z^2 - 3*x^2*y^3*z^2 - y^5*z^2 + 3*x^4*z^3 + 3*x^3*y*z^3 - 3*x^2*y^2*z^3 + 3*x*y^3*z^3 + y^4*z^3 + 3*x^3*z^4 + 2*x^2*y*z^4 - 3*x*y^2*z^4 + 3*y^3*z^4 + x^2*z^5 + 3*x*y*z^5 + y^2*z^5 + 3*x*z^6 - 2*z^7 - 4/45*x^6 - 2*x^5*y + x^4*y^2 - 2*x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 - x^5*z - 2*x^4*y*z - 3*x^3*y^2*z + 3*x^2*y^3*z - 2*x*y^4*z + 2*y^5*z - 3*x^4*z^2 - x^3*y*z^2 - 2*x^2*y^2*z^2 - 3*y^4*z^2 + 3*x^3*z^3 - y^3*z^3 - 3*x*y*z^4 + 3*y^2*z^4 + x*z^5 - 3*y*z^5 - 3*z^6 + x^4*y + 4*x^3*y^2 - x^2*y^3 - 3*x*y^4 - 3*y^5 + x^4*z - x^3*y*z + 3*x*y^3*z + y^4*z - 3*x^3*z^2 + x*y^2*z^2 - 2*y^3*z^2 - 3*x*y*z^3 + x*z^4 + 3*z^5 - 2*x^3*y - 2*x^2*y^2 + x*y^3 - 2*y^4 + 3*x^3*z + x^2*y*z - x*y^2*z + 2*y^3*z + 2*x^2*z^2 + 3*x*y*z^2 + y^2*z^2 + x*z^3 + 3*y*z^3 + z^4 + 2*y^2*z - 2*x*z^2 + y*z^2 + 3*z^3, -3*x^7 - 3*x^6*y - 2*x^5*y^2 - 2*x^4*y^3 + x^3*y^4 + 3*x^2*y^5 - 3*x*y^6 - 2*y^7 - x^5*y*z - x^4*y^2*z + 2*x^3*y^3*z - 3*x^2*y^4*z - 2*x*y^5*z + 2*y^6*z + 2*x^5*z^2 + x^4*y*z^2 + 2*x^3*y^2*z^2 + 2*x^2*y^3*z^2 - x*y^4*z^2 - 2*x^4*z^3 - 3*x^3*y*z^3 + 3*x^2*y^2*z^3 + 3*x*y^3*z^3 - 3*y^4*z^3 + x^3*z^4 + 3*x^2*y*z^4 - 3*x*y^2*z^4 - 2*y^3*z^4 + 3*x^2*z^5 - 2*x*y*z^5 - y^2*z^5 + 3*x*z^6 + 3*y*z^6 + z^7 - 5/48*x^6 - 3*x^4*y^2 - x^2*y^4 - 2*x*y^5 - 3*y^6 - 2*x^5*z + 2*x^4*y*z - x^3*y^2*z - x^2*y^3*z - x*y^4*z + 3*y^5*z - x^4*z^2 + x^3*y*z^2 - x^2*y^2*z^2 + 3*x*y^3*z^2 - y^4*z^2 + 2*x^3*z^3 - 2*x^2*y*z^3 - x^2*z^4 + 2*x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - y*z^5 - z^6 - 3*x^4*y - 10*x^3*y^2 + 2*x^2*y^3 + 2*x*y^4 + y^5 + 3*x^4*z + 3*x^3*y*z + 2*x^2*y^2*z + 3*x*y^3*z + y^4*z + x^3*z^2 + x^2*y*z^2 + 2*x*y^2*z^2 + y^3*z^2 + 3*x^2*z^3 - 3*x*y*z^3 + y^2*z^3 - x*z^4 + 3*y*z^4 + 2*z^5 + 4*x^3*y - 10*x^2*y^2 - 2*x*y^3 + 2*y^4 + 3*x^3*z + 3*x^2*y*z - 2*x*y^2*z - 2*y^3*z + 2*x^2*z^2 - 2*x*y*z^2 + 2*x*z^3 - 2*y*z^3 + 3*z^4 - x*y*z + y^2*z - 2*y*z^2 + 3*z^3, -3*x^7 + 3*x^6*y - x^5*y^2 - 3*x^4*y^3 + x^3*y^4 + x^2*y^5 + 2*x*y^6 + 3*y^7 + 2*x^6*z - x^5*y*z - 3*x^4*y^2*z + 2*x^3*y^3*z + 3*x^2*y^4*z + 2*x*y^5*z - 3*x^5*z^2 - 3*x^4*y*z^2 + 2*x^3*y^2*z^2 + x^2*y^3*z^2 - 2*x*y^4*z^2 + y^5*z^2 + 3*x^4*z^3 - 2*x^3*y*z^3 + 2*x^2*y^2*z^3 + y^4*z^3 - x^3*z^4 + 2*x^2*y*z^4 - 3*x*y^2*z^4 - 3*y^3*z^4 + 3*x^2*z^5 - 2*x*y*z^5 - 2*y^2*z^5 + x*z^6 + y*z^6 + z^7 - 1/144*x^6 + 2*x^5*y + 3*x^4*y^2 + x^3*y^3 + y^6 + x^5*z - 2*x^4*y*z + x^3*y^2*z - 2*x^2*y^3*z + 2*x*y^4*z + 2*y^5*z + 3*x^4*z^2 - 3*x^3*y*z^2 - 3*x^2*y^2*z^2 - 3*x*y^3*z^2 + 2*y^4*z^2 - 3*x^3*z^3 - 3*x^2*y*z^3 - x*y^2*z^3 - y^3*z^3 - x^2*z^4 - x*y*z^4 + y^2*z^4 - x*z^5 - y*z^5 - z^6 + 2*x^4*y + 6*x^3*y^2 - 3*x*y^4 + 3*y^5 + 2*x^3*y*z - x^2*y^2*z - 3*x*y^3*z + 3*y^4*z - 2*x^3*z^2 + 2*x^2*y*z^2 - 3*x*y^2*z^2 - 3*y^3*z^2 - 3*x^2*z^3 + 3*x*y*z^3 - 3*x*z^4 + 2*y*z^4 + 2*z^5 + 6*x^3*y - 8*x^2*y^2 - 3*x*y^3 + 2*y^4 + 2*x^3*z + 2*x^2*y*z + 2*x*y^2*z - y^3*z - 3*x^2*z^2 + x*y*z^2 + x*z^3 + 2*y*z^3 + 3*z^4 + x*y*z - 3*y^2*z - x*z^2 - 3*y*z^2 + z^3]
  [ok] (F2 orbit) G = X*Y^4 + X^4*Z: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [3*x^7 + 3*x^5*y^2 - 2*x^3*y^4 + 2*x*y^6 + 3*y^7 + 3*x^6*z - x^5*y*z - 2*x^4*y^2*z + 2*x^3*y^3*z - x*y^5*z + 2*y^6*z - 3*x^5*z^2 + 2*x^4*y*z^2 + x^3*y^2*z^2 - x^2*y^3*z^2 - 3*x*y^4*z^2 - 3*y^5*z^2 - x^4*z^3 + 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + 3*x*y^3*z^3 - 2*y^4*z^3 - 3*x^3*z^4 - x^2*y*z^4 + x*y^2*z^4 + y^3*z^4 + x^2*z^5 + 2*x*y*z^5 - 2*y^2*z^5 - 2*y*z^6 - 7/360*x^6 + x^5*y + x^4*y^2 + x^3*y^3 + x^2*y^4 - 2*x*y^5 - y^6 - x^5*z - 3*x^4*y*z + x^3*y^2*z - 3*x^2*y^3*z - x*y^4*z - 2*y^5*z - 3*x^4*z^2 - 3*x^2*y^2*z^2 + x*y^3*z^2 - y^4*z^2 + x^3*z^3 + x^2*y*z^3 - 2*x*y^2*z^3 - 2*y^3*z^3 + 3*x^2*z^4 + 2*x*y*z^4 + 3*y^2*z^4 + 3*x*z^5 - 3*y*z^5 + z^6 + 3*x^4*y - x^3*y^2 + 2*x^2*y^3 + 2*x*y^4 - 3*y^5 - 2*x^4*z - 2*x^2*y^2*z - 2*x*y^3*z + y^4*z + 2*x^3*z^2 + 3*x^2*y*z^2 + 3*x*y^2*z^2 + 2*y^3*z^2 + 3*x^2*z^3 + 2*x*y*z^3 + y^2*z^3 + 3*x*z^4 - 3*y*z^4 - z^5 + 3*x^3*y - x^2*y^2 - y^4 + x^3*z - x*y^2*z + 2*y^3*z + 3*x*y*z^2 + y^2*z^2 - 2*x*z^3 - 2*y*z^3 - 3*z^4 - 2*x*y*z + 3*y^2*z + 2*x*z^2 + y*z^2 - z^3, -x^7 - 2*x^6*y + 3*x^4*y^3 + 2*x^2*y^5 - 3*x*y^6 - 2*y^7 - 2*x^6*z - x^5*y*z + 2*x^4*y^2*z - 3*x^2*y^4*z - 2*x*y^5*z + 2*y^6*z - x^5*z^2 + x^4*y*z^2 - x^3*y^2*z^2 - 3*x*y^4*z^2 - x^4*z^3 - 2*x^3*y*z^3 - 2*x^2*y^2*z^3 - 3*x*y^3*z^3 - y^4*z^3 - x^3*z^4 - x^2*y*z^4 - x*y^2*z^4 + 2*y^3*z^4 - 3*x^2*z^5 - 2*x*y*z^5 - y^2*z^5 + 2*x*z^6 - y*z^6 - 2*z^7 + 31/240*x^6 + x^5*y + x^3*y^3 + 3*x^2*y^4 - 2*y^6 - x^5*z + 2*x^3*y^2*z - 2*y^5*z - 2*x^3*y*z^2 - 2*x^2*y^2*z^2 + x*y^3*z^2 + 3*y^4*z^2 + x*y^2*z^3 - 2*y^2*z^4 - x*z^5 + 3*y*z^5 + 3*z^6 + 3*x^4*y - 2*x^3*y^2 - 3*x^2*y^3 + x*y^4 + y^5 - x^4*z + x^3*y*z + 3*x^2*y^2*z + x*y^3*z + y^4*z - x^2*y*z^2 - 2*y^3*z^2 - 2*x^2*z^3 - 3*x*y*z^3 + y^2*z^3 - 2*x*z^4 + 3*y*z^4 - z^5 + x^3*y + x^2*y^2 + 3*y^4 - 3*x^3*z + 3*x^2*y*z - 2*x*y^2*z - y^3*z + 2*x^2*z^2 - 2*x*y*z^2 + 3*y^2*z^2 + 2*x*z^3 + 3*y*z^3 + 2*z^4 - 3*x*y*z + 3*y^2*z - 2*x*z^2 + 2*y*z^2 + 3*z^3, 2*x^7 + 3*x^6*y - 2*x^5*y^2 + 3*x^4*y^3 - 2*x^3*y^4 + 3*x^2*y^5 - y^7 - 2*x^6*z - 2*x^4*y^2*z + x^3*y^3*z - 3*x^2*y^4*z + 2*x*y^5*z + y^6*z - x^5*z^2 - x^4*y*z^2 + 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 + 2*y^5*z^2 + x^4*z^3 - 3*x^3*y*z^3 - x^2*y^2*z^3 + x*y^3*z^3 + 3*y^4*z^3 - x^3*z^4 + 3*x*y^2*z^4 - 2*y^3*z^4 + x^2*z^5 - x*y*z^5 + 3*y^2*z^5 - 2*x*z^6 - y*z^6 - 2*z^7 - 41/720*x^6 - 3*x^5*y - 2*x^4*y^2 + 3*x^3*y^3 + x^2*y^4 - 2*x*y^5 + 3*y^6 + x^2*y^3*z - 3*x*y^4*z + 3*y^5*z - 2*x^4*z^2 - 3*x^2*y^2*z^2 - x*y^3*z^2 + y^4*z^2 - 2*x^3*z^3 - 2*x^2*y*z^3 - 3*x*y^2*z^3 - 2*y^3*z^3 + x*y*z^4 - 3*x*z^5 - z^6 + 3*x^3*y^2 - 3*x^2*y^3 - x*y^4 + y^5 + x^4*z - 3*y^4*z + x^3*z^2 - 2*x^2*y*z^2 - 3*x*y^2*z^2 - y^3*z^2 - x*y*z^3 + y^2*z^3 + 2*x*z^4 - y*z^4 + 2*z^5 + x^3*y + 3*x^2*y^2 + 3*y^4 - 3*x^3*z + x^2*y*z - 2*x*y^2*z - y^3*z - 3*x^2*z^2 + 3*x*y*z^2 - 3*y^2*z^2 + y*z^3 + 2*z^4 - x*y*z - 3*y^2*z - y*z^2 - z^3]
  [ok] (F2 orbit) G = X^2*Y^3 + X^4*Z: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-2*x^6*y + x^5*y^2 - 3*x^4*y^3 - 3*x^3*y^4 - x^2*y^5 - x*y^6 + y^7 + 3*x^6*z + x^5*y*z + x^4*y^2*z + 3*x^3*y^3*z - x^2*y^4*z + x*y^5*z - y^6*z + x^4*y*z^2 + 3*x^3*y^2*z^2 + x^2*y^3*z^2 - x*y^4*z^2 + 2*y^5*z^2 + 2*x^4*z^3 + 3*x^3*y*z^3 + x^2*y^2*z^3 + 2*y^4*z^3 - x^3*z^4 + 3*x^2*y*z^4 - 3*x*y^2*z^4 + y^3*z^4 + x^2*z^5 - x*y*z^5 - 2*x*z^6 + 2*y*z^6 - 2*z^7 + 11/180*x^6 - x^4*y^2 - 3*x^3*y^3 - x^2*y^4 + x*y^5 + y^6 + x^5*z - x^4*y*z + 2*x^3*y^2*z - 3*x^2*y^3*z + 2*x*y^4*z - 3*y^5*z - x^4*z^2 - 3*x^3*y*z^2 + x*y^3*z^2 - y^4*z^2 + 3*x^3*z^3 - x^2*y*z^3 - 2*x*y^2*z^3 - 3*y^3*z^3 + 3*x*y*z^4 - 3*y^2*z^4 - x*z^5 - 2*y*z^5 + 3*z^6 + 2*x^4*y - 3*x^3*y^2 + 2*x^2*y^3 - 2*x*y^4 - 3*y^5 - x^4*z + 2*x^3*y*z + x^2*y^2*z + y^4*z + x^3*z^2 - 3*x^2*y*z^2 + x*y^2*z^2 - y^3*z^2 + 2*x^2*z^3 + 3*y^2*z^3 - 2*x*z^4 - y*z^4 - 3*z^5 + 2*x^3*y - 2*x*y^3 + 3*y^4 + x^3*z - x*y^2*z - 3*y^3*z - 3*x^2*z^2 - x*y*z^2 - 3*y^2*z^2 - 2*x*z^3 - 2*y*z^3 + 3*z^4 - 3*x*y*z + 2*y^2*z + 2*x*z^2 + 3*y*z^2 - z^3, -x^7 - 3*x^6*y + x^5*y^2 + x^4*y^3 + 3*x^3*y^4 - 2*x^2*y^5 - x*y^6 + y^7 + 2*x^6*z + 2*x^5*y*z + 2*x^4*y^2*z - x^3*y^3*z - 3*x^2*y^4*z - 2*x*y^5*z + 2*y^6*z - 3*x^5*z^2 - 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 - x*y^4*z^2 - 3*x^4*z^3 + x^3*y*z^3 - 3*x^2*y^2*z^3 + 3*x*y^3*z^3 - 2*y^4*z^3 - x^3*z^4 + 3*x^2*y*z^4 + 2*x*y^2*z^4 - 3*y^3*z^4 + 2*x^2*z^5 - x*y*z^5 - 3*x*z^6 + 3*y*z^6 + 3*z^7 - 5/72*x^6 + 2*x^5*y + 2*x^4*y^2 - x^3*y^3 + x*y^5 + 3*x^4*y*z + 3*x^3*y^2*z + 2*x*y^4*z + 3*x^4*z^2 - 2*x^3*y*z^2 + 3*x^2*y^2*z^2 - 3*x*y^3*z^2 + y^4*z^2 + x^2*y*z^3 - 2*x*y^2*z^3 - y^3*z^3 - 2*x^2*z^4 + 2*x*y*z^4 - 2*y^2*z^4 - 3*x*z^5 + 3*z^6 + x^3*y^2 - 2*x^2*y^3 - 3*x*y^4 - y^5 + x^4*z - 3*x^3*y*z - 3*x^2*y^2*z - 3*x*y^3*z - y^4*z - x^3*z^2 - x^2*y*z^2 - 2*x*y^2*z^2 + 3*y^3*z^2 + 3*x^2*z^3 - 3*x*y*z^3 + y^2*z^3 - 2*x*z^4 - y*z^4 + 3*z^5 + 3*x^3*y + 6*x*y^3 + 2*y^4 - 3*x^3*z - 3*x^2*y*z - 2*x*y^2*z - 3*y^3*z - 3*x^2*z^2 - 2*x*y*z^2 + y^2*z^2 + y^2*z + 3*x*z^2 - 3*y*z^2 + z^3, -2*x^7 + x^6*y - 2*x^5*y^2 - 3*x^4*y^3 + 2*x^2*y^5 - x*y^6 - 3*y^7 + 3*x^6*z - x^5*y*z - 3*x^4*y^2*z - 2*x^3*y^3*z + x^2*y^4*z + 2*x*y^5*z + 2*y^6*z - x^5*z^2 - 2*x^4*y*z^2 + x^3*y^2*z^2 - x*y^4*z^2 - x^4*z^3 - x^2*y^2*z^3 + 3*x*y^3*z^3 - y^4*z^3 + 3*x^3*z^4 + x^2*y*z^4 - 2*x*y^2*z^4 + 3*x^2*z^5 + x*y*z^5 - 3*y^2*z^5 + 2*x*z^6 + y*z^6 + 13/120*x^6 + 2*x^5*y - x^4*y^2 + 2*x^3*y^3 - x^2*y^4 - 3*x*y^5 - y^6 - 2*x^5*z - 3*x^4*y*z - x^3*y^2*z + 2*x^2*y^3*z + x*y^4*z - 2*y^5*z + 2*x^4*z^2 + 2*x^3*y*z^2 - x^2*y^2*z^2 - x*y^3*z^2 - 3*y^4*z^2 + 2*x^3*z^3 - 2*x^2*y*z^3 + x*y^2*z^3 - y^3*z^3 + 2*x^2*z^4 - 3*y^2*z^4 + 2*x*z^5 + 3*z^6 + 2*x^4*y - x^3*y^2 + 6*x^2*y^3 + 2*y^5 - 3*x^4*z + 3*x^3*y*z + 3*x^2*y^2*z - 3*x*y^3*z + 3*y^4*z + 3*x^3*z^2 + 3*x^2*y*z^2 - 3*y^3*z^2 + 2*x*y*z^3 + 3*y^2*z^3 - 2*x*z^4 - 3*y*z^4 - 2*z^5 - 2*x^3*y + 2*x*y^3 + 2*y^4 - x^3*z + 2*x^2*y*z - 3*x*y^2*z - y^3*z + 3*x*y*z^2 - 2*y^2*z^2 + 2*x*z^3 + 2*y*z^3 + 2*z^4 - 2*y^2*z - 3*x*z^2 - y*z^2 - 3*z^3]
  [ok] (F2 orbit) G = X^3*Y^2 + X^4*Z: QT(u=-3*x - 3*y + z), triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [2*x^7 + 2*x^6*y - 2*x^5*y^2 - 3*x^4*y^3 + 2*x^3*y^4 + x*y^6 + 2*y^7 - x^6*z + x^5*y*z + 2*x^4*y^2*z - x^3*y^3*z - x^2*y^4*z - 3*x*y^5*z - 2*y^6*z + 3*x^5*z^2 - 3*x^4*y*z^2 - 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 - 3*x*y^4*z^2 - y^5*z^2 - 2*x^4*z^3 + 2*x^3*y*z^3 - 2*x^2*y^2*z^3 - x*y^3*z^3 - 3*x^3*z^4 + x^2*y*z^4 - 3*x*y^2*z^4 - 2*x^2*z^5 + 2*x*y*z^5 + 2*y^2*z^5 + 3*x*z^6 - y*z^6 - 2*z^7 - 13/180*x^6 + 2*x^5*y + 2*x^4*y^2 + 3*x^2*y^4 - 2*x*y^5 - 2*y^6 + x^5*z - 3*x^4*y*z + 2*x^3*y^2*z + 3*x*y^4*z + y^5*z + 2*x^4*z^2 - 3*x^3*y*z^2 - 3*x*y^3*z^2 - 3*x^3*z^3 + x^2*y*z^3 + 3*x*y^2*z^3 + 2*y^3*z^3 + 3*x^2*z^4 + 3*x*y*z^4 + y^2*z^4 + 2*x*z^5 + 2*z^6 + 1/15*x^5 - 3*x^4*y + 22/9*x^3*y^2 - y^5 - x^4*z - 2*x^3*y*z - 3*x^2*y^2*z - 2*x*y^3*z + 2*y^4*z - 3*x^3*z^2 + 3*x^2*y*z^2 - x*y^2*z^2 - 2*y^3*z^2 + x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 - 2*x*z^4 - 2*y*z^4 - 2*z^5 - 6*x^2*y^2 - 3*x*y^3 + 2*y^4 + 3*x^3*z + 3*x*y^2*z - x^2*z^2 - 2*x*y*z^2 + 3*y^2*z^2 - x*z^3 - 3*y*z^3 - 3*z^4 + 3*y^2*z + 3*x*z^2 - z^3, x^7 + 3*x^6*y + 2*x^5*y^2 - x^4*y^3 - x^3*y^4 - 2*x^2*y^5 - 2*x*y^6 + y^7 + 3*x^6*z + x^5*y*z - 3*x^4*y^2*z + 3*x^2*y^4*z - 2*x*y^5*z - 3*y^6*z - x^5*z^2 + 3*x^4*y*z^2 + 3*x^3*y^2*z^2 + x^2*y^3*z^2 - y^5*z^2 + 3*x^2*y^2*z^3 - 2*x^3*z^4 + 2*x^2*y*z^4 + x*y^2*z^4 + 2*y^3*z^4 + 2*x^2*z^5 + 2*x*y*z^5 - 3*x*z^6 + 3*y*z^6 - 2*z^7 + 13/240*x^6 - 3*x^5*y - x^4*y^2 - 2*x^3*y^3 + 3*x^2*y^4 + 2*x*y^5 - 2*y^6 + 2*x^5*z + 3*x^4*y*z - x^2*y^3*z - x*y^4*z + 2*y^5*z - x^4*z^2 - 3*x^3*y*z^2 + 3*x^2*y^2*z^2 + x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 + x^2*y*z^3 - 2*y^3*z^3 + 3*x^2*z^4 + x*y*z^4 + x*z^5 + 3*y*z^5 + 3*z^6 - 13/120*x^5 - 3*x^4*y + 23/18*x^3*y^2 - 2*x^2*y^3 + 3*x*y^4 + y^5 - x^4*z + 2*x^3*y*z + x^2*y^2*z - 3*x*y^3*z + x^3*z^2 - x*y^2*z^2 - 2*y^3*z^2 - 2*x^2*z^3 + 3*x*y*z^3 - 3*y^2*z^3 - 3*x*z^4 - y*z^4 + z^5 + 2*x^2*y^2 - x^3*z - 3*x^2*y*z + 2*y^3*z + x^2*z^2 + 2*x*y*z^2 + y^2*z^2 - x*z^3 + 2*y*z^3 - z^4 + 3*x*y*z - 3*x*z^2 + 2*y*z^2, 3*x^7 - 3*x^6*y + 2*x^5*y^2 + x^4*y^3 + 2*x^3*y^4 - 2*x^2*y^5 - x*y^6 + 2*y^7 - x^6*z + 3*x^5*y*z - 3*y^6*z - x^5*z^2 + 3*x^4*y*z^2 - 2*x^3*y^2*z^2 + 3*x^2*y^3*z^2 - 2*x*y^4*z^2 - 3*x^4*z^3 - 2*x^3*y*z^3 + 3*x^2*y^2*z^3 + 3*x*y^3*z^3 - 2*x^3*z^4 + 3*x^2*y*z^4 - 2*x*y^2*z^4 + 3*x^2*z^5 + y^2*z^5 - x*z^6 + 2*y*z^6 + 3*z^7 - 21/80*x^6 + 2*x^5*y - x^2*y^4 - x*y^5 - 3*y^6 - x^3*y^2*z - x^2*y^3*z - x*y^4*z + 2*x^4*z^2 - x^3*y*z^2 - 3*x^2*y^2*z^2 - 3*x*y^3*z^2 + 2*x^3*z^3 + 2*x^2*y*z^3 + 3*x*y^2*z^3 - y^3*z^3 + 3*x^2*z^4 + 3*x*y*z^4 - 3*y^2*z^4 + 2*x*z^5 + 3*y*z^5 - 3*z^6 - 13/120*x^5 - x^4*y - 121/18*x^3*y^2 - 2*x^2*y^3 - 3*x*y^4 + 3*y^5 + 3*x^4*z + x^3*y*z + 3*x^2*y^2*z - x*y^3*z - 2*y^4*z - 3*x^3*z^2 - 3*x^2*y*z^2 - 3*x*y^2*z^2 + y^3*z^2 - 2*x^2*z^3 + 3*x*y*z^3 - 2*y^2*z^3 - 3*x*z^4 - 2*z^5 - 6*x^2*y^2 + x*y^3 + 2*y^4 + 3*x^3*z - 2*x^2*y*z - x*y^2*z + 2*y^3*z - 2*x^2*z^2 + x*y*z^2 - 3*x*z^3 - 2*y*z^3 + 3*x*y*z + 2*y^2*z - 3*x*z^2 + y*z^2 + 3*z^3]
certified values: {'X^3*Y^2 + Y^5 + X^4*Z': 41, 'Y^5 + X^4*Z': 41, 'X^3*Y^2 + X*Y^4 + X^4*Z': 41, 'X*Y^4 + X^4*Z': 41, 'X^2*Y^3 + X^4*Z': 41, 'X^3*Y^2 + X^4*Z': 41}
10 checks, 0 failed
ALL CHECKS PASSED
