The realization space is
  [1   0   1          1   0   1    0    1            x1    1          x1]
  [0   1   1   2*x1 + 1   0   0    1    1   2*x1^2 + x1   x1   -2*x1 - 1]
  [0   0   0          0   1   1   -1   x1      2*x1 + 1    1    2*x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (16*x1^8 + 40*x1^7 + 24*x1^6 - 26*x1^5 - 49*x1^4 - 31*x1^3 - 9*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[2*x1 + 1, x1 + 1, 2, x1, x1 - 1, x1^2 - 2*x1 - 1, 3*x1 + 1, 2*x1^3 - x1^2 - 2*x1 - 1, 2*x1^2 + 2*x1 + 1, 2*x1 - 1]