# r2_n567.py (independent verification run 2, AI-assisted, own code); p = 2147472617
  n=5 V=[(24, -27), (33, 40), (-40, -24), (-15, 37), (-11, 1)] d=9: monomials 715, rank 715, dim ker E_d = 0  (3s)
  n=5 V=[(24, -27), (33, 40), (-40, -24), (-15, 37), (-11, 1)] d=10: monomials 1001, rank 999, dim ker E_d = 2  (6s)
  n=5 V=[(24, -27), (33, 40), (-40, -24), (-15, 37), (-11, 1)] d=11: monomials 1365, rank 1349, dim ker E_d = 16  (12s)
  n=5 V=[(24, -27), (33, 40), (-40, -24), (-15, 37), (-11, 1)] d=12: monomials 1820, rank 1761, dim ker E_d = 59  (21s)
  n=5 V=[(-18, -20), (-6, -28), (31, 39), (-2, -4), (3, -17)] d=9: monomials 715, rank 715, dim ker E_d = 0  (2s)
  n=5 V=[(-18, -20), (-6, -28), (31, 39), (-2, -4), (3, -17)] d=10: monomials 1001, rank 999, dim ker E_d = 2  (5s)
  n=5 V=[(-18, -20), (-6, -28), (31, 39), (-2, -4), (3, -17)] d=11: monomials 1365, rank 1349, dim ker E_d = 16  (9s)
  n=7 V=[(-11, -23), (-27, -9), (23, 33), (39, -26), (20, -36), (-22, -39), (34, -39)] d=6: monomials 924, rank 924, dim ker E_d = 0  (9s)
  n=7 V=[(-11, -23), (-27, -9), (23, 33), (39, -26), (20, -36), (-22, -39), (34, -39)] d=7: monomials 1716, rank 1708, dim ker E_d = 8  (17s)
