{
  "id": 5583,
  "curve_key": "0:-38157015319835904",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "44163212175736"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 76.36097204708567,
  "faltings_height": 4.421070246382101,
  "conductor": "52660511361335064931572825792",
  "bad_primes": [
    "2",
    "3",
    "406661",
    "13574947"
  ],
  "discriminant": "-842568181781361038905165212672",
  "regulator": "520425652.2295826188312557341780255706037170749230466750495",
  "points": [
    [
      "-33930",
      "2258644"
    ],
    [
      "-20103",
      "6003247"
    ],
    [
      "-16110",
      "6323144"
    ],
    [
      "-7278",
      "6616472"
    ],
    [
      "62337",
      "16923317"
    ],
    [
      "126354",
      "45403160"
    ],
    [
      "-796206/25",
      "430465072/125"
    ],
    [
      "-244814/9",
      "132371920/27"
    ],
    [
      "-122462/9",
      "174236696/27"
    ],
    [
      "20625/4",
      "53246777/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = 59/19 of a Mordell family constructed from the Burkhardt quartic, using the affine quadruple (a,b,c,d) = (-11/2,12,6,3/2).\r\n\r\nFound by varying the Burkhardt quartic parameters using the rational parametrization of Bruin–Nasserden, followed by a sixth-power-residue Mestre–Nagao sieve.\r\n\r\nPARI/GP 2.17.4 verifies exact rank 10, with bounds [10,10] and 10 rational points.",
  "created_at": "2026-10-23 20:01:05",
  "updated_at": "2026-10-23 20:01:05"
}