The realization space is
  [1   0   1   0   1    0          x1 + 1                 x1 + 1          x1 + 1          x1 + 1          1]
  [0   1   1   0   0    1          x1 + 1                     x1              x1   x1^2 + x1 + 1         x1]
  [0   0   0   1   1   -1   x1^2 + x1 + 1   x1^3 + x1^2 + x1 + 1   x1^2 + x1 + 1              x1   x1^2 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^4 + x1^3 + x1^2 + x1 + 1, -x1^6 - 2*x1^5 - 3*x1^4 - 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1^3 + x1^2 + 1, x1^6 + x1^5 + 3*x1^4 + 2*x1^3 + 2*x1^2 + 2*x1 + 1, x1^4 + x1^3 + x1^2 + x1 + 2, x1^2 + x1 + 1, x1^3 + x1 + 1, x1, x1^4 + x1 + 1, 2*x1^10 + 3*x1^9 + 8*x1^8 + 12*x1^7 + 19*x1^6 + 18*x1^5 + 25*x1^4 + 21*x1^3 + 17*x1^2 + 10*x1 + 9, 2*x1^6 + x1^5 + 4*x1^4 + 4*x1^3 + 5*x1^2 + 2*x1 + 3, 2*x1^6 + x1^5 + 5*x1^4 + 5*x1^3 + 6*x1^2 + 3*x1 + 5, 2*x1^8 + 3*x1^7 + 7*x1^6 + 10*x1^5 + 13*x1^4 + 11*x1^3 + 11*x1^2 + 6*x1 + 3, 2*x1^6 + x1^5 + 5*x1^4 + 4*x1^3 + 5*x1^2 + 3*x1 + 4, 2*x1^8 + 3*x1^7 + 5*x1^6 + 9*x1^5 + 8*x1^4 + 7*x1^3 + 6*x1^2 + 3*x1 - 1, 2*x1^6 + x1^5 + 4*x1^4 + 4*x1^3 + 4*x1^2 + 2*x1 + 4, x1^2 + 1, 2*x1^7 + x1^6 + 5*x1^5 + 5*x1^4 + 5*x1^3 + 3*x1^2 + 4*x1 - 1, x1 - 1, 2*x1^6 + x1^5 + 5*x1^4 + 5*x1^3 + 6*x1^2 + 4*x1 + 5, 2*x1^6 + x1^5 + 5*x1^4 + 5*x1^3 + 5*x1^2 + 2*x1 + 4, 2*x1^6 + x1^5 + 5*x1^4 + 4*x1^3 + 4*x1^2 + 3*x1 + 5, x1 + 1, x1^4 + x1^3 + 2*x1^2 + 3*x1 + 2, x1^4 + x1^3 + 2*x1^2 + 2*x1 + 1, 3*x1^7 + 3*x1^6 + 8*x1^5 + 10*x1^4 + 11*x1^3 + 7*x1^2 + 7*x1 + 2, x1^7 + 2*x1^5 - 2*x1^2 - x1 - 3, 4*x1^12 + 4*x1^11 + 21*x1^10 + 30*x1^9 + 59*x1^8 + 73*x1^7 + 109*x1^6 + 97*x1^5 + 112*x1^4 + 83*x1^3 + 66*x1^2 + 29*x1 + 24, 2*x1^10 + 3*x1^9 + 10*x1^8 + 16*x1^7 + 27*x1^6 + 32*x1^5 + 41*x1^4 + 35*x1^3 + 29*x1^2 + 17*x1 + 10, x1^4 + x1^3 + 2*x1^2 + 2*x1 + 2, 2*x1^6 + x1^5 + 4*x1^4 + 4*x1^3 + 4*x1^2 + x1 + 3, 2*x1^6 + x1^5 + 5*x1^4 + 5*x1^3 + 6*x1^2 + 3*x1 + 4, 4*x1^12 + 4*x1^11 + 19*x1^10 + 27*x1^9 + 49*x1^8 + 58*x1^7 + 82*x1^6 + 68*x1^5 + 73*x1^4 + 51*x1^3 + 38*x1^2 + 13*x1 + 12, 4*x1^6 + 2*x1^5 + 9*x1^4 + 8*x1^3 + 9*x1^2 + 5*x1 + 8, 2*x1^6 + x1^5 + 4*x1^4 + 3*x1^3 + 3*x1^2 + 2, 2*x1^6 + x1^5 + 4*x1^4 + 3*x1^3 + 3*x1^2 + x1 + 3, 2*x1^6 + x1^5 + 5*x1^4 + 5*x1^3 + 6*x1^2 + 5*x1 + 6]