{
  "id": 4461,
  "curve_key": "1473:1215",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-31",
    "6"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 21.88516924938789,
  "faltings_height": -0.10802354784772476,
  "conductor": "1848689",
  "bad_primes": [
    "191",
    "9679"
  ],
  "discriminant": "1848689",
  "regulator": "10.48075399525355228684810192165702824857912873",
  "points": [
    [
      "-3",
      "9"
    ],
    [
      "-2",
      "8"
    ],
    [
      "0",
      "2"
    ],
    [
      "12",
      "29"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "BASE records/rank_4.md#16 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.",
  "created_at": "2026-10-17 10:24:59",
  "updated_at": "2026-10-17 10:24:59"
}