{
  "standard_basis": [
    "1",
    "a",
    "b",
    "c",
    "d",
    "e",
    "a^2",
    "ab",
    "ac",
    "ad"
  ],
  "quadratic_relations": [
    "ae-a^2",
    "3b^2-ab-10ac",
    "bc-3ad",
    "3bd-8a^2+ad",
    "3be-a^2+4ab",
    "c^2-3a^2",
    "cd-a^2+2ab",
    "ce+ac",
    "3d^2+ab+4ac",
    "3de-ac+2ad",
    "3e^2+a^2-2ad"
  ],
  "quadratic_basis_determinant": "-1",
  "cubic_multiple_rank_QQ": 35,
  "linear_syzygy_dimension": 20,
  "weight1_constraint_shape": [
    80,
    55
  ],
  "weight1_constraint_rank_QQ": 49,
  "weight2_constraint_shape": [
    100,
    11
  ],
  "weight2_constraint_rank_QQ": 11,
  "cubic_nonzero_minor": {
    "prime": 32003,
    "rank": 35,
    "rows": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      8,
      7,
      9,
      13,
      10,
      16,
      12,
      15,
      14,
      11,
      17,
      20,
      19,
      18,
      21,
      22,
      23,
      24,
      25,
      26,
      27,
      28,
      29,
      30,
      31,
      32,
      33,
      34
    ],
    "columns": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20,
      21,
      22,
      23,
      24,
      27,
      28,
      29,
      33,
      34,
      39,
      43,
      44,
      49,
      54
    ],
    "determinant": 21492
  },
  "weight1_nonzero_minor": {
    "prime": 32003,
    "rank": 49,
    "rows": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20,
      22,
      21,
      23,
      24,
      25,
      26,
      27,
      28,
      29,
      36,
      37,
      39,
      33,
      35,
      38,
      31,
      51,
      40,
      48,
      50,
      64,
      52,
      43,
      49,
      65,
      67,
      68,
      66
    ],
    "columns": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20,
      21,
      22,
      23,
      24,
      25,
      26,
      27,
      28,
      29,
      30,
      31,
      32,
      33,
      34,
      35,
      36,
      37,
      38,
      39,
      41,
      42,
      43,
      44,
      46,
      47,
      48,
      49,
      52
    ],
    "determinant": 9763
  },
  "weight2_nonzero_minor": {
    "prime": 32003,
    "rank": 11,
    "rows": [
      0,
      1,
      2,
      3,
      4,
      10,
      11,
      25,
      45,
      60,
      80
    ],
    "columns": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10
    ],
    "determinant": 4926
  }
}
All assertions passed. Smoothable family and tangent dimension <=44+6=50 verified.
Since the smoothable component has dimension50, the Hilbert point is smooth.
