The realization space is
  [1   0   1   0   1   0                     x1^2                                                          x1^3                                           x1^2                                           x1^2                                                          x1^3]
  [1   1   0   1   0   0   x1^2 - x1*x2 - x1 + x2   -x1^3*x2 + x1^2*x2^2 + 2*x1^2*x2 - 2*x1*x2^2 - x1*x2 + x2^2   -x1^3 + x1^2*x2 + 2*x1^2 - 2*x1*x2 - x1 + x2   -x1^3 + x1^2*x2 + 2*x1^2 - 2*x1*x2 - x1 + x2   -x1^3*x2 + x1^2*x2^2 + 2*x1^2*x2 - 2*x1*x2^2 - x1*x2 + x2^2]
  [1   1   0   0   1   1                        0                              -x1^4 + x1^3*x2 + x1^3 - x1^2*x2                 -x1^3 + x1^2*x2 + x1^2 - x1*x2                                           x1^3                                                       x1^3*x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - x2, 2*x1^3 - x1^2*x2 - 2*x1^2 + 2*x1*x2 + x1 - x2, x2, x1 - 1, x1^2 - x1 + x2, 2*x1^2 - x1*x2 - x1 + x2, 2*x1^5*x2 - 3*x1^4*x2^2 - 3*x1^4*x2 + x1^4 + x1^3*x2^3 + 7*x1^3*x2^2 + x1^3*x2 - x1^3 - 3*x1^2*x2^3 - 5*x1^2*x2^2 + x1^2*x2 + 3*x1*x2^3 + x1*x2^2 - x2^3, 2*x1^3*x2 + x1^3 - x1^2*x2^2 - 3*x1^2*x2 - x1^2 + 2*x1*x2^2 + 2*x1*x2 - x2^2, 2*x1^2*x2 - x1^2 - x1*x2^2 + x2^2, x1*x2 + x1 - x2, x1^2 - x1*x2 + x2, x2 - 1, 2*x1^3*x2 - x1^3 - x1^2*x2^2 - 2*x1^2*x2 + 2*x1*x2^2 + x1*x2 - x2^2, x1^3 - x1^2*x2 - x1^2 + 2*x1*x2 + x1 - x2, x1, 3*x1^4 - 3*x1^3*x2 - 3*x1^3 + x1^2*x2^2 + 5*x1^2*x2 + x1^2 - 2*x1*x2^2 - 2*x1*x2 + x2^2, x1^4 - 2*x1^3*x2 + x1^2*x2^2 + 3*x1^2*x2 - 2*x1*x2^2 - x1*x2 + x2^2]