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What do you expect? The transformation from V-representation to H-representation is not a trivial one. This coefficient blowup might already seen when looking at solution to linear equations

sage: M = matrix(5, 6, [[2,1,0,0,0,0],
....:                   [0,2,1,0,0,0],
....:                   [0,0,2,1,0,0],
....:                   [0,0,0,2,1,0],
....:                   [0,0,0,0,2,1]])
sage: M
[2 1 0 0 0 0]
[0 2 1 0 0 0]
[0 0 2 1 0 0]
[0 0 0 2 1 0]
[0 0 0 0 2 1]
sage: M.right_kernel()
Free module of degree 6 and rank 1 over Integer Ring
Echelon basis matrix:
[  1  -2   4  -8  16 -32]