{
  "id": 5683,
  "curve_key": "0:-31457498406781176",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "36409141674515"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 75.97482754549593,
  "faltings_height": 4.388891537916289,
  "conductor": "261851969871589756596804441",
  "bad_primes": [
    "3",
    "568163",
    "9493661"
  ],
  "discriminant": "-572670258109166797677211312467",
  "regulator": "135318171075.7055350497176271402641493918417284104902454005",
  "points": [
    [
      "9249/4",
      "48280181/8"
    ],
    [
      "-16959042327/538756",
      "903339615173729/395446904"
    ],
    [
      "-240624723/27889",
      "27854144033729/4657463"
    ],
    [
      "-50673695/5184",
      "2223102284207/373248"
    ],
    [
      "-43511/100",
      "6033991487/1000"
    ],
    [
      "102205545/256",
      "1033560470965/4096"
    ],
    [
      "225609585/16384",
      "13100096481143/2097152"
    ],
    [
      "481730145/3364",
      "10638526131283/195112"
    ],
    [
      "134978343/5041",
      "2668934529743/357911"
    ],
    [
      "746805651/121",
      "20408516032262/1331"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Mordell curve obtained by specializing a rationally parametrized Burkhardt-quartic rank-4 family at (u,v,w) = (1/2,-1,2/3), t = -22/71.\r\n\r\nPARI/GP 2.17.4 returned matching rank bounds [10,10].",
  "created_at": "2026-10-24 09:02:26",
  "updated_at": "2026-10-24 09:02:26"
}