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