{
  "id": 5728,
  "curve_key": "0:966831280838568",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-1119017686156"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 69.01009023851975,
  "faltings_height": 3.8084967623349413,
  "conductor": "247348263097159230659409",
  "bad_primes": [
    "3",
    "281",
    "589965829"
  ],
  "discriminant": "-540950651393487237452127483",
  "regulator": "29107070.544833611644608191488271679992828837576735420125",
  "points": [
    [
      "10446",
      "144355"
    ],
    [
      "10608",
      "273307"
    ],
    [
      "11212",
      "538916"
    ],
    [
      "11356",
      "587739"
    ],
    [
      "52449/4",
      "8524355/8"
    ],
    [
      "17736",
      "2111899"
    ],
    [
      "26052",
      "4069723"
    ],
    [
      "36196",
      "6804644"
    ],
    [
      "395412",
      "248639908"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed by specializing a rank-four Mordell family obtained from a rational parametrization of the Burkhardt quartic.\r\n\r\nThe construction parameters are (u,v,w) = (-5,4,-2), with specialization t = -141/74.\r\n\r\nAn archived PARI/GP 2.17.4 computation returned matching rank bounds [9,9] together with nine rational points. ",
  "created_at": "2026-10-24 17:00:14",
  "updated_at": "2026-10-24 17:00:14"
}