The realization space is
  [1   1   0   0   1   1         0          4        4        2        2]
  [1   0   1   0   1   0         2     x1 + 3   x1 + 3   x1 + 5   x1 + 1]
  [0   0   0   1   1   1   -x1 - 3   2*x1 + 2       -4       -2     2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^2 + 6*x1 + 1, -8*x1^3 - 40*x1^2 + 40*x1 + 8)
avoiding the zero loci of the polynomials
RingElem[x1^2 + 4*x1 - 1, x1 + 1, 2, x1 + 5, x1 - 1, x1^2 + 6*x1 - 3, x1 + 7, x1 + 2, x1^2 + 5*x1 + 2, x1 + 3, x1^2 + 10*x1 + 5, x1^2 + 8*x1 + 3, x1^2 + 8*x1 - 1, 3*x1 - 1, x1, x1^2 + 7*x1 + 8, x1^2 + 8*x1 + 11, x1^2 + 2*x1 - 11, x1^2 + 2*x1 - 19, x1 - 5, x1^2 + 10*x1 + 13, 3*x1 + 1]