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