The realization space is
  [1   1   0                    1   0   1   1                 0                    1                 1                 1]
  [1   0   1   4*x1^2 + 15*x1 - 5   0   1   0                 1   4*x1^2 + 15*x1 - 5   x1^2 + 4*x1 - 1   x1^2 + 4*x1 - 1]
  [0   0   0                    0   1   1   1   x1^2 + 3*x1 - 2      x1^2 + 4*x1 - 1   x1^2 + 4*x1 - 1                x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^3 + 3*x1^2 - 4*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[x1^2 + 4*x1 - 2, x1^2 + 3*x1 - 1, x1^2 + 4*x1 - 1, x1 + 4, 3*x1 - 1, x1^4 + 4*x1^3 - 2*x1^2 - 6*x1 + 2, x1^4 + 4*x1^3 + x1^2 + 5*x1 - 2, x1^4 + 4*x1^3 + 2*x1^2 + 8*x1 - 3, 3*x1^4 + 20*x1^3 + 22*x1^2 - 37*x1 + 9, x1^4 + 7*x1^3 + 9*x1^2 - 12*x1 + 2, x1^2 + 3*x1 - 2, 3*x1^4 + 20*x1^3 + 23*x1^2 - 33*x1 + 8, x1^4 + 7*x1^3 + 8*x1^2 - 15*x1 + 5, x1^4 + 7*x1^3 + 9*x1^2 - 12*x1 + 3, x1^2 + 5*x1 - 2, x1 - 1, 4*x1^3 + 12*x1^2 - 17*x1 + 4, 4*x1^2 + 15*x1 - 6, x1, 4*x1^2 + 15*x1 - 5, x1^4 + 7*x1^3 + 7*x1^2 - 18*x1 + 5, x1^2 + 3*x1 - 3, 3*x1^4 + 20*x1^3 + 24*x1^2 - 30*x1 + 7, 2*x1^2 + 8*x1 - 3, 4*x1^4 + 31*x1^3 + 48*x1^2 - 46*x1 + 9, 4*x1^4 + 27*x1^3 + 30*x1^2 - 52*x1 + 13, 4*x1^4 + 27*x1^3 + 31*x1^2 - 49*x1 + 11, 4*x1^4 + 27*x1^3 + 30*x1^2 - 52*x1 + 14, 4*x1^3 + 11*x1^2 - 13*x1 + 3, 5*x1^2 + 19*x1 - 7, 4*x1^4 + 27*x1^3 + 32*x1^2 - 45*x1 + 11, 4*x1^4 + 27*x1^3 + 31*x1^2 - 48*x1 + 13]