The realization space is
  [1   1   0           1   1   0    1    0          1           1           1]
  [0   1   1   -5*x1 + 4   0   0    0    1   5*x1 - 3           1    5*x1 - 3]
  [0   0   0           0   1   1   x1   -1          1   -5*x1 + 3   -5*x1 + 3]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (5*x1^2 - 6*x1 + 2, -125*x1^4 + 425*x1^3 - 480*x1^2 + 222*x1 - 36)
avoiding the zero loci of the polynomials
RingElem[5*x1 - 4, 5*x1 - 3, 5*x1 - 2, 3, 2*x1 - 1, 10*x1 - 7, x1, 5*x1^2 - 9*x1 + 3, 35*x1^2 - 42*x1 + 12, x1 - 1, 5*x1^2 - 5*x1 + 1, 5, 2, 15*x1^2 - 17*x1 + 5, 3*x1 - 2, 5*x1^2 - 4*x1 + 1]