{
  "id": 5586,
  "curve_key": "0:4262725390509989335296",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-4933709942719895064"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 99.60839134325126,
  "faltings_height": 6.3583551877292335,
  "conductor": "36289369535338444294503260444736",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "978917",
    "2817677"
  ],
  "discriminant": "-10515525321121840900839730239002115689472",
  "regulator": "1245416267175.26743200259561479901524722022600943124899265858",
  "points": [
    [
      "1871142",
      "1271802168"
    ],
    [
      "4363450",
      "8839968956"
    ],
    [
      "5559450",
      "12918781044"
    ],
    [
      "21183162",
      "97470556092"
    ],
    [
      "62608105/4",
      "495069606773/8"
    ],
    [
      "687852321/25",
      "18038124040131/125"
    ],
    [
      "29917275738/16129",
      "2464962455336724/2048383"
    ],
    [
      "142302305929/63001",
      "40594284485393345/15813251"
    ],
    [
      "991356220009/215296",
      "961798472950984885/99897344"
    ],
    [
      "8054421821754/1311025",
      "22614215619219746508/1501123625"
    ],
    [
      "35865760043841/20025625",
      "80712039033424301139/89614671875"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = 11/9 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, with rational parametrization parameters (u,v,w) = (5,4,-2).\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 11, with bounds [11,11] and 11 independent rational points.",
  "created_at": "2026-10-23 20:59:36",
  "updated_at": "2026-10-23 20:59:36"
}