The realization space is
  [1   0   1   1                   x2 - 1    1   0   x2 - 1          0                   x2 - 1      x2 - 1]
  [0   1   1   1   x2^3 - 2*x2^2 + x2 - 1   x2   0        0     x2 - 1   x2^3 - 2*x2^2 + x2 - 1   x2^2 - x2]
  [0   0   0   1   x2^3 - 2*x2^2 + x2 - 1    1   1   x1 - 1   -x1 + x2               x1*x2 - x1      x1 - 1]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (-2*x1 + x2^2 - x2 + 1, 2*x1^2 - 2*x1*x2 + x2)
avoiding the zero loci of the polynomials
RingElem[2*x1^2*x2 - x1*x2^3 + x1*x2^2 - 3*x1*x2 - x1 + x2^2 + 1, x1*x2 - 2*x1 + 1, 2*x1^2*x2 - x1*x2^3 + 2*x1*x2^2 - 6*x1*x2 + x1 + x2^2 + x2, 2*x1^2*x2 - x1*x2^3 - 4*x1*x2 + x1 + 2*x2^3 - 2*x2^2 + 3*x2 - 1, x1*x2 + x1 - x2^2 - 1, 2*x1*x2 - 2*x2^2 + x2 - 1, x1 - x2, x2, 2*x1^2*x2 - 3*x1*x2^2 - 2*x1*x2 + x1 + 2*x2^3 - x2^2 + 2*x2 - 1, x1*x2 - x2^2 + x2 - 1, x1 - 1, 2*x1*x2 - x1 - x2^2, x2 - 1, 2*x1*x2 - x2^2 - 1, x1 - x2^2 + x2 - 1, 2*x1^2*x2 - 2*x1*x2^3 + 3*x1*x2^2 - 5*x1*x2 + x2^4 - 2*x2^3 + 3*x2^2 - x2 + 1, 2*x1 - x2 - 1, 2*x1^2*x2 - 2*x1*x2^2 - 3*x1*x2 + x1 + x2^3 + x2^2, 2*x1^2*x2 - 2*x1*x2^2 - 3*x1*x2 + x1 + x2^3 + 2*x2 - 1, 2*x1^2*x2 - 3*x1*x2^2 - x1*x2 + 2*x2^3 - 2*x2^2 + 3*x2 - 1, 2*x1^2*x2 - 5*x1*x2 + x1 + x2^2 + x2, x1*x2^2 - 3*x1*x2 + x2^2 + 1, x1*x2^2 - 4*x1*x2 + x1 + x2^2 + x2, x1, x1 - x2 + 1, 2*x1^2*x2 - 2*x1*x2^2 - x1*x2 - x1 + x2^3 - x2^2 + 2*x2, 2*x1^2*x2 - x1*x2^2 - 3*x1*x2 + 2*x2^2 - x2 + 1, 2*x1^2*x2 + 2*x1*x2^3 - 6*x1*x2^2 + x1*x2 - x1 - x2^4 + 2*x2^3 + x2, 2*x1^2*x2 + x1*x2^2 - 5*x1*x2 - x2^3 + 2*x2^2 + 1]