The realization space is
  [1   1   0   0   1   1           0   2*x1^2 - 3*x1 + 1      x1 - 1         2*x1^2 - x1           x1^2 - x1]
  [1   0   1   0   1   0    2*x1 - 1   4*x1^2 - 4*x1 + 1    2*x1 - 1   4*x1^2 - 4*x1 + 1   4*x1^2 - 4*x1 + 1]
  [0   0   0   1   1   1   x1^2 - x1         x1^3 - x1^2   x1^2 - x1                x1^3         x1^3 - x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (8*x1^10 - 44*x1^9 + 70*x1^8 - 17*x1^7 - 64*x1^6 + 78*x1^5 - 40*x1^4 + 10*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1^3 + 2*x1^2 - 3*x1 + 1, x1, 2*x1 - 1, x1 - 1, x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1^2 - 3*x1 + 1, x1^2 - 3*x1 + 1, x1^2 + x1 - 1]