The realization space is
  [1   1   0                            x2^2   0   1   1                               0                            x2^2                                   x2^2    1]
  [1   0   1   -2*x1^2*x2 + x1^2 + 2*x1*x2^2   0   1   0                         x1 - x2   -2*x1^2*x2 + x1^2 + 2*x1*x2^2   2*x1^2*x2 - x1^2 - 2*x1*x2^2 + x1*x2   x1]
  [0   0   0                               0   1   1   1   -4*x1*x2 + 2*x1 + 4*x2^2 - x2     -2*x1*x2^2 + x1*x2 + 2*x2^3            -2*x1*x2^2 + x1*x2 + 2*x2^3   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[4*x1^2*x2 - 2*x1^2 - 4*x1*x2^2 - x1*x2 + x1 + x2^2, 4*x1*x2 - 2*x1 - 4*x2^2 + x2, x1, 2*x1*x2 - x1 - x2^2, 2*x1^2*x2 - x1^2 - x1*x2^2 - x2^3, 2*x2 - 1, 2*x1*x2 - x1 - 3*x2^2 + x2, x1 - x2, 8*x1^3*x2^2 - 8*x1^3*x2 + 2*x1^3 - 20*x1^2*x2^3 + 14*x1^2*x2^2 - 2*x1^2*x2 + 12*x1*x2^4 - 4*x1*x2^3 - x2^4, 2*x1*x2 - x1 - 2*x2^2, 4*x1^2*x2 - 2*x1^2 - 4*x1*x2^2 + 2*x1*x2 - x2^2, 4*x1^2*x2 - 2*x1^2 - 4*x1*x2^2 - 2*x1*x2 + 2*x1 + 3*x2^2 - x2, 4*x1^2*x2 - 2*x1^2 - 4*x1*x2^2 - 2*x1*x2 + x1 + 3*x2^2, 4*x1^2*x2 - 2*x1^2 - 4*x1*x2^2 + 2*x1*x2 - x1 - x2^2 + x2, x1 + x2 - 1, x2 - 1, x1*x2 - x1 - x2^2, x1 - 1, 2*x1^2*x2^2 - 3*x1^2*x2 + x1^2 - 2*x1*x2^3 + x1*x2^2 + x2^3, 2*x1*x2 - x1 - x2, x2, 8*x1^3*x2^2 - 8*x1^3*x2 + 2*x1^3 - 16*x1^2*x2^3 + 12*x1^2*x2^2 - 2*x1^2*x2 + 8*x1*x2^4 - 6*x1*x2^3 + 2*x1*x2^2 + 2*x2^4 - x2^3, 16*x1^3*x2^2 - 16*x1^3*x2 + 4*x1^3 - 32*x1^2*x2^3 + 22*x1^2*x2^2 - 3*x1^2*x2 + 16*x1*x2^4 - 4*x1*x2^3 - 2*x2^4, 4*x1^2*x2 - 2*x1^2 - 4*x1*x2^2 + x2^2, 2*x1^2*x2 - x1^2 - 2*x1*x2^2 + x1*x2 - x2^2, 2*x1^2*x2 - x1^2 - 2*x2^3, 4*x1^3*x2^2 - 4*x1^3*x2 + x1^3 - 8*x1^2*x2^3 + 8*x1^2*x2^2 - 2*x1^2*x2 + 4*x1*x2^4 - 2*x1*x2^3 - 2*x2^4, 2*x1^2*x2 - x1^2 - x1*x2 - 2*x2^3 + x2^2, 4*x1*x2 - 3*x1 - 4*x2^2 + 2*x2, 8*x1^3*x2^2 - 8*x1^3*x2 + 2*x1^3 - 16*x1^2*x2^3 + 10*x1^2*x2^2 - x1^2*x2 + 8*x1*x2^4 - 2*x1*x2^3 + x1*x2^2 - x2^3, 4*x1*x2 - x1 - 4*x2^2, 8*x1^2*x2^2 - 8*x1^2*x2 + 2*x1^2 - 8*x1*x2^3 + 2*x1*x2^2 + x1*x2 + 4*x2^3]