The realization space is
  [1    1   1   1   0   x1 - 1   0            x1            x1                         0       x1 - 1]
  [1   x1   0   0   1      -x1   0            x1          x1^2               2*x1^2 - x1          -x1]
  [1   x1   0   1   0        0   1   -x1*x2 + x2   -x1*x2 + x2   -x1^2*x2 + 2*x1*x2 - x2   x1*x2 - 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 - 1, x1 - x2, x1^2*x2 + 2*x1^2 - 3*x1*x2 - x1 + x2, x2, x1, x1*x2 - 2*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, x1^3*x2 - x1^3 - 4*x1^2*x2 + 4*x1*x2 - x2, x1^2 + x1*x2 - x2, x1^2*x2 - x1^2 - 2*x1*x2 + x2, 2*x1 - 1, x1*x2 + x1 - x2, x2 - 1, x1^3*x2 - 5*x1^2*x2 - 2*x1^2 + 6*x1*x2 + x1 - 2*x2, x1^2 - 3*x1 + 1, x1^3*x2 - 4*x1^2*x2 - 2*x1^2 + 4*x1*x2 + x1 - x2, x1*x2 + 2*x1 - x2 - 1, x1^2*x2 + 2*x1^2 - 2*x1*x2 - x1 + x2, x1^3 + 2*x1^2*x2 - 3*x1*x2 + x2]