{
  "id": 4459,
  "curve_key": "1641:-47925",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-34",
    "64"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 22.209183273270273,
  "faltings_height": -0.12428689749093189,
  "conductor": "614066",
  "bad_primes": [
    "2",
    "307033"
  ],
  "discriminant": "1228132",
  "regulator": "21.22549118520972037736431059618969688069510816",
  "points": [
    [
      "-6",
      "8"
    ],
    [
      "-5",
      "12"
    ],
    [
      "-3",
      "13"
    ],
    [
      "19",
      "68"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "BASE records/rank_4.md#5 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.",
  "created_at": "2026-10-17 10:24:53",
  "updated_at": "2026-10-17 10:24:53"
}