The realization space is
  [1   0   1   1   0   1   1   0   1   1   1]
  [0   1   1   3   0   0   0   1   1   2   2]
  [0   0   0   0   1   1   2   4   3   1   2]
in the integer ring
within the vanishing set of the ideal
5ZZ
avoiding the zero loci of the polynomials
RingElem[2, 3, 7, 11]