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Among the 128 solutions found, only 2 are integer solutions:

sage: len(sol)
128
sage: def is_integer_solution(solution):
....:     return all(eq.rhs() in ZZ for eq in solution)
....:     
sage: integer_solutions = [s for s in sol if is_integer_solution(s)]
sage: len(integer_solutions)
2
sage: integer_solutions
[[x == 127,
  y == -254,
  N == 1019,
  M == 32512,
  F == 30496,
  f == -63,
  G == 32016,
  g == -31,
  L == 32392,
  l == -15,
  Q == 32484,
  q == -7,
  S == 32506,
  s == -3,
  U == 32511,
  u == -1],
 [x == 127,
  y == 255,
  N == 1019,
  M == 32512,
  F == 30496,
  f == -63,
  G == 32016,
  g == -31,
  L == 32392,
  l == -15,
  Q == 32484,
  q == -7,
  S == 32506,
  s == -3,
  U == 32511,
  u == -1]]

In Python, you can filter a list using list comprehension. Among the 128 solutions found, only 2 are integer solutions:

sage: len(sol)
128
sage: def is_integer_solution(solution):
....:     return all(eq.rhs() in ZZ for eq in solution)
....:     
sage: integer_solutions = [s for s in sol if is_integer_solution(s)]
sage: len(integer_solutions)
2
sage: integer_solutions
[[x == 127,
  y == -254,
  N == 1019,
  M == 32512,
  F == 30496,
  f == -63,
  G == 32016,
  g == -31,
  L == 32392,
  l == -15,
  Q == 32484,
  q == -7,
  S == 32506,
  s == -3,
  U == 32511,
  u == -1],
 [x == 127,
  y == 255,
  N == 1019,
  M == 32512,
  F == 30496,
  f == -63,
  G == 32016,
  g == -31,
  L == 32392,
  l == -15,
  Q == 32484,
  q == -7,
  S == 32506,
  s == -3,
  U == 32511,
  u == -1]]