The realization space is
  [1   0   1    2*x1 - 1   0   1    0        x1^2             2*x1 - 1   2*x1 - 1      2*x1 - 1]
  [0   1   1   x1^2 - x1   0   0    1        x1^2            x1^2 - x1      -x1^2         -x1^2]
  [0   0   0           0   1   1   -1   -2*x1 + 1   -2*x1^2 + 3*x1 - 1   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 (8*x1^11 - 44*x1^10 + 102*x1^9 - 81*x1^8 - 16*x1^7 + 62*x1^6 - 38*x1^5 + 10*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 + 2*x1 - 1, 2*x1 - 1, x1^3 + 2*x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^2 - 5*x1 + 2, x1^2 - 3*x1 + 1, x1^3 - x1^2 - 2*x1 + 1]