The realization space is
  [1   1   0   -2   0   1   1          0      -2   2*x1 - 3   2*x1 - 3]
  [0   1   1   -1   0   0   1   2*x1 - 2      -1   2*x1 - 2         -1]
  [0   0   0    0   1   1   1         -1   -2*x1         -1         -1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-48*x1^4 + 200*x1^3 - 300*x1^2 + 190*x1 - 42)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, 4*x1^2 - 8*x1 + 5, 2, 6*x1 - 5, x1 - 1, 2*x1 - 3, 4*x1^2 - 4*x1 - 1, 4*x1 - 3, 4*x1 - 5]