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