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 integer ring
avoiding the zero loci of the polynomials
RingElem[2, 3, 5]