The realization space is
  [1   1   0   1   0   1   1    0   1    1]
  [0   1   1   3   0   0   1    1   3   -3]
  [0   0   0   0   1   1   1   -1   3    3]
in the multivariate polynomial ring in 0 variables over ZZ
within the vanishing set of the ideal
Ideal (12)
avoiding the zero loci of the polynomials
RingElem[3, 2, 5]