The realization space is
  [1   0   1   x1 - x2   0   1    0   x1 - x2        x1 - x2   x1 - x2        x1 - x2]
  [0   1   1     x1*x2   0   0    1   x1 - x2          x1*x2      x2^2           x2^2]
  [0   0   0         0   1   1   -1      x2^2   x1^2 - x1*x2   x1 - x2   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, x2 - 1, x1 - x2^2 - x2, x1 - x2, x1, x1^2 - 2*x1*x2 - x2^3 + x2^2, x1 - 2*x2, x1*x2 - x1 + x2, x1 - 1, x1^2 - x1*x2^2 - x1 + x2, x1 + x2 - 1, x1 + x2^2 - x2, x1^2 - x1*x2 - x2^2, x1^3 - x1^2*x2 - x1^2 - x1*x2^3 + 2*x1*x2 - x2^2, x1^2 - x1 + x2, x1^2*x2 - x1^2 - x1*x2^3 - x1*x2^2 + 2*x1*x2 - x2^2]