{
  "id": 5689,
  "curve_key": "0:-324892762394328",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "376033289808"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 66.82903256389058,
  "faltings_height": 3.626741956115843,
  "conductor": "20361749046338207998334601",
  "bad_primes": [
    "3",
    "1531",
    "982451443"
  ],
  "discriminant": "-61085247139014623995003803",
  "regulator": "25073374.446570834711850793423712443603787115932334004626",
  "points": [
    [
      "-7216",
      "17071"
    ],
    [
      "-5812",
      "423919"
    ],
    [
      "-5526",
      "455288"
    ],
    [
      "-3816",
      "566096"
    ],
    [
      "-1906",
      "607543"
    ],
    [
      "-828",
      "612752"
    ],
    [
      "5297/4",
      "4920845/8"
    ],
    [
      "2438",
      "624919"
    ],
    [
      "16313/4",
      "5329841/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Mordell curve constructed by specializing a rank-4 Burkhardt-quartic family using the Bruin–Nasserden parametrization (u,v,w)=(3/4,5/4,-3/4), with t=36/23.\r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [9,9].",
  "created_at": "2026-10-24 10:09:58",
  "updated_at": "2026-10-24 10:09:58"
}