{
  "id": 5721,
  "curve_key": "0:334770107925888",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-387465402692"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 66.88893033436477,
  "faltings_height": 3.6317334369886933,
  "conductor": "4053494833648390462865328",
  "bad_primes": [
    "2",
    "3",
    "96866350673"
  ],
  "discriminant": "-64855917338374247405845248",
  "regulator": "43805023.522748652939187651909228742528607948879896222633",
  "points": [
    [
      "7317",
      "65389"
    ],
    [
      "7677",
      "254929"
    ],
    [
      "7842",
      "307886"
    ],
    [
      "11922",
      "1143266"
    ],
    [
      "30546",
      "5302238"
    ],
    [
      "55866",
      "13189802"
    ],
    [
      "68466",
      "17904002"
    ],
    [
      "65938/9",
      "2055302/27"
    ],
    [
      "136138/9",
      "47335598/27"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed by specializing a rank-four Mordell family arising from the rational parametrization of the Burkhardt quartic. The construction parameters are (u,v,w) = (7,-2,10), with specialization t = -59/76.\r\n\r\nPARI/GP 2.17.4 returned matching rank bounds [9,9] and nine rational points. ",
  "created_at": "2026-10-24 16:42:28",
  "updated_at": "2026-10-24 16:42:28"
}