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