{
  "id": 5588,
  "curve_key": "0:28139702160024648",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-32569099722251"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 75.75191572464009,
  "faltings_height": 4.3703155528449695,
  "conductor": "152747460967379598834429006081",
  "bad_primes": [
    "3",
    "139",
    "2777",
    "337501001"
  ],
  "discriminant": "-458242382902138796503287018243",
  "regulator": "825494747.5152503954580245217412297504216342040799660024150",
  "points": [
    [
      "31943",
      "155267"
    ],
    [
      "32077",
      "660313"
    ],
    [
      "32347",
      "1129816"
    ],
    [
      "131297/4",
      "13378851/8"
    ],
    [
      "34691",
      "3029904"
    ],
    [
      "43543",
      "7070227"
    ],
    [
      "117551",
      "39897099"
    ],
    [
      "199693",
      "89054182"
    ],
    [
      "208567",
      "95079628"
    ],
    [
      "1138873/4",
      "1214524583/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = -8/137 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, with rational parametrization parameters (u,v,w) = (7,-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 10, with bounds [10,10] and 10 independent rational points.",
  "created_at": "2026-10-23 21:01:22",
  "updated_at": "2026-10-23 21:01:22"
}