{
  "id": 5592,
  "curve_key": "0:-488673387306976896",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "565594198271964"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 81.46094148322048,
  "faltings_height": 4.846067699393336,
  "conductor": "3949343174307478086465536016",
  "bad_primes": [
    "2",
    "3",
    "5236983317333"
  ],
  "discriminant": "-138195416355367273201602036271872",
  "regulator": "310632628.9965224954508018031716480980649852247998680536753",
  "points": [
    [
      "-82662",
      "874206"
    ],
    [
      "-67515",
      "16057467"
    ],
    [
      "-60630",
      "18512658"
    ],
    [
      "-10979",
      "23754385"
    ],
    [
      "45858",
      "25729974"
    ],
    [
      "75450",
      "31545342"
    ],
    [
      "153021",
      "64409985"
    ],
    [
      "473538",
      "326727594"
    ],
    [
      "-25791/4",
      "190212705/8"
    ],
    [
      "484617/4",
      "387313947/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = 247/229 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, with affine parameters (a,b,c,d) = (4/5,-24/5,6,-9) and generating parameters (u,v,w) = (-1,-4,5).\r\n\r\nFound using a sixth-power-residue Mestre–Nagao sieve across Burkhardt surface parameters, with 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 21:28:54",
  "updated_at": "2026-10-23 21:28:54"
}