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