The realization space is
  [1   1   0                   1   0   1   1                 0                   1                 1                 1]
  [1   0   1   3*x1^2 + 8*x1 - 4   0   1   0                 1   3*x1^2 + 8*x1 - 4   x1^2 + 3*x1 - 1   x1^2 + 3*x1 - 1]
  [0   0   0                   0   1   1   1   x1^2 + 2*x1 - 1     x1^2 + 3*x1 - 1   x1^2 + 3*x1 - 1                x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^3 + 2*x1^2 - 3*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[x1^2 + 3*x1 - 2, x1^2 + 2*x1 - 1, x1^2 + 3*x1 - 1, x1 + 3, 2*x1 - 1, x1^3 + 4*x1^2 + 2*x1 - 2, x1 - 1, x1^4 + 3*x1^3 + x1 - 1, x1^4 + 3*x1^3 + x1^2 + 3*x1 - 2, 2*x1^2 + 5*x1 - 4, x1^2 + 2*x1 - 2, x1^4 + 5*x1^3 + 4*x1^2 - 6*x1 + 1, 2*x1^4 + 9*x1^3 + 5*x1^2 - 10*x1 + 3, x1^4 + 5*x1^3 + 4*x1^2 - 6*x1 + 2, x1^2 + 4*x1 - 2, 3*x1^3 + 6*x1^2 - 10*x1 + 3, 3*x1^2 + 8*x1 - 5, x1, 3*x1^2 + 8*x1 - 4, x1^4 + 5*x1^3 + 2*x1^2 - 10*x1 + 3, 2*x1^4 + 9*x1^3 + 6*x1^2 - 8*x1 + 2, 2*x1^2 + 6*x1 - 3, 3*x1^4 + 17*x1^3 + 15*x1^2 - 25*x1 + 7, 3*x1^4 + 14*x1^3 + 7*x1^2 - 21*x1 + 6, 3*x1^4 + 14*x1^3 + 8*x1^2 - 19*x1 + 5, 3*x1^4 + 14*x1^3 + 7*x1^2 - 21*x1 + 7, 3*x1^3 + 5*x1^2 - 7*x1 + 2, 4*x1^2 + 11*x1 - 6, x1 + 2, 3*x1^4 + 14*x1^3 + 9*x1^2 - 16*x1 + 5, 3*x1^4 + 14*x1^3 + 8*x1^2 - 18*x1 + 6]