{
  "id": 4498,
  "curve_key": "12976:-7724440",
  "ainvs": [
    "0",
    "1",
    "1",
    "-270",
    "8850"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 31.719799772422064,
  "faltings_height": 0.700361274755021,
  "conductor": "33265115083",
  "bad_primes": [
    "137",
    "3413",
    "71143"
  ],
  "discriminant": "-33265115083",
  "regulator": "279.23221272974514850285958251331558844425843807012",
  "points": [
    [
      "-25",
      "24"
    ],
    [
      "-23",
      "58"
    ],
    [
      "-21",
      "75"
    ],
    [
      "6",
      "86"
    ],
    [
      "12",
      "86"
    ],
    [
      "24",
      "129"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "BASE records/rank_6.md#18 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.",
  "created_at": "2026-10-17 10:31:35",
  "updated_at": "2026-10-17 10:31:35"
}