The realization space is
  [1   1   0   0   1   1   0   2   2   2   2]
  [0   1   1   1   2   3   0   0   2   4   6]
  [0   1   1   0   0   1   1   1   1   3   3]
in the integer ring
avoiding the zero loci of the polynomials
RingElem[3, 2, 7, 5]