The realization space is
  [1   1    1   0   0   1   1    1   0    2]
  [0   1   -1   1   0   0   1   -1   1   -3]
  [0   0    0   0   1   1   2    2   2    2]
in the integer ring
avoiding the zero loci of the polynomials
RingElem[2, 3, 5]