{
  "id": 5794,
  "curve_key": "0:-639961205236017912",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "740695839393539"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 82.00036790521682,
  "faltings_height": 4.891019901226363,
  "conductor": "641251020813674852592574641",
  "bad_primes": [
    "3",
    "13",
    "649306017439"
  ],
  "discriminant": "-237008301045796666542773365037523",
  "regulator": "8855482781113.373831246879742236815334665017917994691326703",
  "points": [
    [
      "-486972833439/5382400",
      "3775806674606191/12487168000"
    ],
    [
      "-30546417606743/358042084",
      "74126633368685663561/6774872313448"
    ],
    [
      "-54981923593143/1441872784",
      "1433225498475042395941/54750793354048"
    ],
    [
      "-227303150439/10176100",
      "876798668235170191/32461759000"
    ],
    [
      "55057308513/14318656",
      "1474653527276014993/54181794304"
    ],
    [
      "40920974213809/2831304100",
      "4108497464193608342877/150653691161000"
    ],
    [
      "384284982561/18490000",
      "2176914422148665809/79507000000"
    ],
    [
      "1120176320353/26460736",
      "3889535153621348463/136114025984"
    ],
    [
      "2707703066977/40551424",
      "8321305751823984529/258231468032"
    ],
    [
      "-101086583119837743/1949731883584",
      "66760383238233986328285209/2722465221541079552"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rationally 3-isogenous partner of the specialization t = -975/928 of the generic rank-four Burkhardt Mordell family with construction parameters (-9, 8, -2).\r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [10,10], consistent with the independent rank lower bound of ten.",
  "created_at": "2026-10-25 10:32:18",
  "updated_at": "2026-10-25 10:32:18"
}