{
  "id": 5587,
  "curve_key": "0:-15983176524951197016",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "18499046903878700"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 88.43613675152525,
  "faltings_height": 5.427333971752066,
  "conductor": "8163020482154546866896024441",
  "bad_primes": [
    "3",
    "7",
    "13",
    "71",
    "20389",
    "228617"
  ],
  "discriminant": "-147836766104022582296623194751879227",
  "regulator": "170652592.6661126163857766366533065157083085456658302022949",
  "points": [
    [
      "-264432",
      "2971363"
    ],
    [
      "-73164",
      "134563747"
    ],
    [
      "-41090",
      "135755924"
    ],
    [
      "-19292",
      "135984803"
    ],
    [
      "455217/4",
      "1130606123/8"
    ],
    [
      "174048",
      "154179868"
    ],
    [
      "6946836",
      "18310177372"
    ],
    [
      "-5425446/25",
      "11373085967/125"
    ],
    [
      "-4084626/25",
      "14862671807/125"
    ],
    [
      "-31850/9",
      "3672298025/27"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = 89/82 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, with rational parametrization parameters (u,v,w) = (-4,7,8).\r\n\r\nFound by varying the Burkhardt parameters using the rational parametrization of Bruin–Nasserden, followed by a sixth-power-residue Mestre–Nagao sieve, 3-isogeny deduplication, and conductor-aware candidate selection.\r\n\r\nPARI/GP 2.17.4 establishes exact rank 10, with bounds [10,10] and 10 independent rational points.",
  "created_at": "2026-10-23 21:00:31",
  "updated_at": "2026-10-23 21:00:31"
}