The realization space is
  [1   0   1      1   0   1    0       x1    1]
  [0   1   1   x1^2   0   0   x1       x1   x1]
  [0   0   0      0   1   1    1   x1 + 1    1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^6 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1 + 1]