The realization space is
  [1   1   0   0   1   1          0           1             3*x1 - 1         1          1]
  [0   1   1   0   0   1   3*x1 - 1   -4*x1 + 2   -3*x1^2 + 4*x1 - 1   -x1 + 1         x1]
  [0   0   0   1   1   1        -x1    3*x1 - 1   -4*x1^2 + 4*x1 - 1      2*x1   3*x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (5*x1^2 - 4*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[30*x1^2 - 29*x1 + 9, x1, 15*x1^2 - 13*x1 + 4, 15*x1^2 - 14*x1 + 4, 30*x1^3 - 59*x1^2 + 36*x1 - 8, 30*x1^3 - 44*x1^2 + 23*x1 - 4, 225*x1^4 - 450*x1^3 + 341*x1^2 - 119*x1 + 16, 15*x1^2 - 17*x1 + 5, 15*x1^2 - 10*x1 + 2, 90*x1^4 - 147*x1^3 + 100*x1^2 - 32*x1 + 4, 90*x1^4 - 102*x1^3 + 31*x1^2 + 3*x1 - 2, 15*x1^2 - 13*x1 + 3, 3*x1 - 2, 15*x1^2 - 17*x1 + 6, 3*x1 - 1, 15*x1^3 - 22*x1^2 + 9*x1 - 1, 15*x1^3 - 37*x1^2 + 22*x1 - 4, 15*x1^3 - 22*x1^2 + 12*x1 - 2, 15*x1^3 - 37*x1^2 + 25*x1 - 5, 2*x1 - 1, x1 - 1, 2, 225*x1^4 - 435*x1^3 + 334*x1^2 - 123*x1 + 19, 225*x1^4 - 435*x1^3 + 319*x1^2 - 110*x1 + 15, 225*x1^4 - 435*x1^3 + 334*x1^2 - 120*x1 + 18, 225*x1^4 - 435*x1^3 + 304*x1^2 - 97*x1 + 12, 225*x1^4 - 435*x1^3 + 304*x1^2 - 94*x1 + 11, 30*x1^2 - 23*x1 + 6, 15*x1^2 - 10*x1 + 3, 675*x1^5 - 1755*x1^4 + 1827*x1^3 - 968*x1^2 + 262*x1 - 29, 675*x1^5 - 1755*x1^4 + 1782*x1^3 - 899*x1^2 + 227*x1 - 23, 225*x1^4 - 435*x1^3 + 334*x1^2 - 120*x1 + 17, 225*x1^4 - 435*x1^3 + 334*x1^2 - 117*x1 + 16, 225*x1^4 - 435*x1^3 + 319*x1^2 - 104*x1 + 13, 6*x1^2 - 4*x1 + 1, 90*x1^3 - 114*x1^2 + 51*x1 - 8, 45*x1^3 - 60*x1^2 + 29*x1 - 5, 75*x1^3 - 95*x1^2 + 38*x1 - 5, 5*x1 - 3, 5*x1 - 2, 15*x1^2 - 16*x1 + 5]