{
  "id": 5751,
  "curve_key": "0:36343969053119208",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-42064778996666"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 76.26360934373679,
  "faltings_height": 4.412956687769694,
  "conductor": "1507693319606626100946419409",
  "bad_primes": [
    "3",
    "13",
    "17",
    "58565651231"
  ],
  "discriminant": "-764400513040559433179834640363",
  "regulator": "1669883813.854683607130395813930258074055705721474990308810",
  "points": [
    [
      "45032",
      "7018173"
    ],
    [
      "47632",
      "8124226"
    ],
    [
      "333593/4",
      "185557303/8"
    ],
    [
      "100126",
      "31011610"
    ],
    [
      "173732",
      "72122498"
    ],
    [
      "176696",
      "73990845"
    ],
    [
      "2761057/36",
      "4368771611/216"
    ],
    [
      "1480726/25",
      "1609131026/125"
    ],
    [
      "3306056/25",
      "5956336954/125"
    ],
    [
      "2320665334/37249",
      "101606589283333/7189057"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed using the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(6/8,7/8,-5/8) and specialization t=-641/625. \r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [10,10].",
  "created_at": "2026-10-24 18:44:22",
  "updated_at": "2026-10-24 18:44:22"
}