The realization space is
  [1   0   1   1        x1 - 1      1   0    1         0   2*x1 - 2       2*x1]
  [0   1   1   1   2*x1^2 - x1   2*x1   0    0         1         -1   2*x1 - 1]
  [0   0   0   1   2*x1^2 - x1      1   1   x1   -x1 + 1     x1 - 1         x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^2 - 2*x1 + 1, 16*x1^8 - 52*x1^7 + 72*x1^6 - 56*x1^5 + 26*x1^4 - 7*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 4*x1^2 - 3*x1 + 1, 2*x1 - 1, x1 - 1, 4*x1^2 - 6*x1 + 3, 4*x1^2 - 6*x1 + 1, 3*x1 - 1, 2, 8*x1^2 - 4*x1 + 1, 4*x1 - 1, 8*x1^3 - 10*x1^2 + 4*x1 - 1, 2*x1^2 - 2*x1 + 1, 4*x1^2 - 4*x1 + 3, 2*x1^2 - x1 + 1, 2*x1^2 - 3*x1 + 2, 3*x1^2 - 3*x1 + 1, 2*x1^3 - 2*x1^2 + 2*x1 - 1]