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