The realization space is
  [1   1   x1 - 1   0   0   1    1              x1 - 1                   0                     1                    1]
  [0   1       -1   1   0   0    1                  -1                   1    5*x1^2 - 11*x1 + 4   5*x1^2 - 11*x1 + 4]
  [0   0        0   0   1   1   x1   5*x1^2 - 8*x1 + 2   5*x1^2 - 9*x1 + 2   -5*x1^2 + 11*x1 - 3                   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (5*x1^3 - 11*x1^2 + 6*x1 - 1, -25*x1^6 + 125*x1^5 - 254*x1^4 + 277*x1^3 - 171*x1^2 + 52*x1 - 6)
avoiding the zero loci of the polynomials
RingElem[5*x1^2 - 10*x1 + 3, 5*x1^2 - 11*x1 + 4, 5*x1^2 - 11*x1 + 3, 5*x1^3 - 16*x1^2 + 15*x1 - 3, 25*x1^4 - 100*x1^3 + 129*x1^2 - 59*x1 + 8, 25*x1^4 - 100*x1^3 + 124*x1^2 - 50*x1 + 6, 25*x1^5 - 125*x1^4 + 229*x1^3 - 183*x1^2 + 58*x1 - 6, 5*x1^2 - 9*x1 + 2, 25*x1^5 - 125*x1^4 + 224*x1^3 - 167*x1^2 + 44*x1 - 3, 25*x1^5 - 135*x1^4 + 261*x1^3 - 218*x1^2 + 75*x1 - 9, 5*x1^2 - 11*x1 + 5, x1, x1 - 1, 25*x1^4 - 100*x1^3 + 134*x1^2 - 69*x1 + 11, 5*x1^2 - 9*x1 + 3, 25*x1^5 - 125*x1^4 + 234*x1^3 - 198*x1^2 + 71*x1 - 9, 5*x1^3 - 6*x1^2 - 7*x1 + 3, 5*x1^3 - 21*x1^2 + 23*x1 - 5, 7*x1^2 - 12*x1 + 3, 5*x1^3 - 21*x1^2 + 24*x1 - 6, 3*x1 - 1, 2*x1 - 3, 5*x1^2 - 10*x1 + 2, 5*x1^3 - 16*x1^2 + 13*x1 - 3]