The realization space is
  [1   1   0   0   1   1                   0       2*x1 - 1      2*x1 - 1           2*x1 - 1           2*x1 - 1]
  [0   1   1   0   0   1            2*x1 - 1           x1^3          x1^3   -x1^2 + 2*x1 - 1   -x1^2 + 2*x1 - 1]
  [0   0   0   1   1   1   -x1^3 - x1^2 + x1   -x1^3 + x1^2   2*x1^2 - x1   -x1^3 + 2*x1 - 1        2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^3 + 2*x1^2 - 3*x1 + 1, x1, x1^3 + x1^2 - 2*x1 + 1, x1^2 + x1 - 1, x1^2 + 2*x1 - 1, x1^5 - 2*x1^4 - 5*x1^3 + 9*x1^2 - 5*x1 + 1, x1^2 + 2*x1 - 2, x1^4 - x1^3 - 6*x1^2 + 7*x1 - 2, x1^4 - 6*x1^2 + 5*x1 - 1, x1^5 + x1^4 - 5*x1^3 + 8*x1^2 - 5*x1 + 1, 3*x1^2 - 3*x1 + 1, x1^6 - 6*x1^4 + 3*x1^3 + 4*x1^2 - 4*x1 + 1, x1^6 - 2*x1^4 + 7*x1^3 - 9*x1^2 + 5*x1 - 1, x1^6 + 2*x1^5 + x1^3 - 5*x1^2 + 4*x1 - 1, x1^5 + 2*x1^4 - 3*x1^3 - x1^2 + 3*x1 - 1, x1^6 + x1^5 - 3*x1^4 + 5*x1^3 - 6*x1^2 + 4*x1 - 1, x1^6 + 2*x1^5 - 2*x1^4 - 2*x1^2 + 3*x1 - 1, x1^2 + 3*x1 - 2, x1^3 - x1^2 + 2*x1 - 1, x1^6 + x1^5 - x1^4 + 4*x1^3 - 8*x1^2 + 5*x1 - 1, x1^5 + 2*x1^4 - x1^3 + 2*x1^2 - 3*x1 + 1, x1^3 + 3*x1^2 - 1, x1^6 + x1^5 - 5*x1^4 + 2*x1^3 - 2*x1^2 + 3*x1 - 1, 2*x1 - 1, x1^3 + x1^2 + x1 - 1]