The realization space is
  [1   1   0     x1 - 1   0   1   -x1^2 + 2*x1 - 1   1        0         1           x1^2 + x1 - 1]
  [0   1   1   2*x1 - 1   0   0                  0   1   x1 - 1   -x1 + 1   -x1^3 + 4*x1^2 - 2*x1]
  [0   0   0          0   1   1       -2*x1^2 + x1   1      -x1        x1        x1^3 + x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^10 - 16*x1^9 + 49*x1^8 - 95*x1^7 + 101*x1^6 - 58*x1^5 + 17*x1^4 - 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, x1^2 - 4*x1 + 2, 3*x1 - 2, 3*x1^3 - 4*x1^2 + 3*x1 - 1, x1^3 + 5*x1^2 - 5*x1 + 1, x1^4 - 3*x1^3 + 7*x1^2 - 5*x1 + 1, x1^2 + x1 - 1]