The realization space is
  [1   0   1    x1^2 - 2*x1 + 1   0   1    0    1    x1^2 - 2*x1 + 1   x1 - 1   x1 - 1]
  [0   1   1   -2*x1^2 - x1 + 1   0   0    1    1   -2*x1^2 - x1 + 1    -2*x1    -2*x1]
  [0   0   0                  0   1   1   -1   x1          x1^2 + x1   x1 - 1     2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-72*x1^11 + 102*x1^10 + 82*x1^9 - 186*x1^8 + 50*x1^7 + 66*x1^6 - 58*x1^5 + 18*x1^4 - 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[2, x1, x1 + 1, 3*x1 - 1, x1 - 3, 2*x1^2 - x1 + 1, 2*x1 - 1, 4*x1^3 - x1^2 + 2*x1 - 1, x1 - 1]