The realization space is
  [1   0   1   0   1    0           2   -2*x1 - 2            4   -2*x1 - 2         2]
  [0   1   1   0   0    1           2   -5*x1 + 1     7*x1 - 1    4*x1 - 2   -x1 + 1]
  [0   0   0   1   1   -1   -7*x1 + 3     -x1 - 1   -14*x1 + 6     -x1 - 1      2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (7*x1^2 - 4*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, 7*x1 - 1, 21*x1^2 - 12*x1 + 1, 7*x1 - 3, 21*x1^2 - 19*x1 + 6, 2, 7*x1 - 5, 49*x1^2 - 70*x1 + 17, 7*x1 - 4, 14*x1^2 - 8*x1 + 3, 14*x1^2 - 8*x1 + 1, 7*x1 + 3, 7*x1^2 - 4*x1 + 3, 7*x1^2 + 3*x1 - 2, 49*x1^2 - 56*x1 + 23, 98*x1^3 - 119*x1^2 + 64*x1 - 15, 14*x1^2 - 15*x1 + 5, 98*x1^3 - 119*x1^2 + 50*x1 - 13, 14*x1^2 - 7*x1 + 3, 14*x1^2 - 7*x1 + 1, 14*x1^2 - 9*x1 + 3, x1 - 1, x1, 42*x1^2 - 31*x1 + 11, 42*x1^2 - 31*x1 + 7, 294*x1^3 - 385*x1^2 + 208*x1 - 41, 21*x1 - 5, 42*x1^2 - 31*x1 + 9, 14*x1^2 - x1 + 1, 14*x1^2 - 15*x1 + 3, 98*x1^3 - 63*x1^2 + 4*x1 - 7, 7*x1 - 11, 14*x1^2 - x1 + 3, 14*x1^2 - x1 - 1, 14*x1^2 - 15*x1 + 7]