The realization space is
  [1   1   0   0   1   1      0      2                   1      2*x1^2 - 2*x1 + 1                1]
  [0   1   1   0   0   1   2*x1   2*x1   2*x1^2 - 2*x1 + 1   2*x1^3 - 2*x1^2 + x1   -2*x1^2 + 2*x1]
  [0   0   0   1   1   1      1      1                  x1                   x1^2               x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-16*x1^8 + 56*x1^7 - 84*x1^6 + 66*x1^5 - 26*x1^4 + 4*x1^3)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 - 1, 4*x1^2 - 2*x1 + 1, 2, 2*x1^2 - 2*x1 + 1, 4*x1^2 - 3*x1 + 1, 4*x1^2 - 6*x1 + 3, x1^2 - x1 + 1, 2*x1 + 1]