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