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