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