{
  "id": 5326,
  "curve_key": "0:497886238728",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-576257221"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 53.86727490317273,
  "faltings_height": 2.546595484389356,
  "conductor": "186707339523",
  "bad_primes": [
    "3",
    "53",
    "523"
  ],
  "discriminant": "-143455270089534147603",
  "regulator": "1705.881665039014467241318701248544390042655613",
  "points": [
    [
      "4057",
      "257291"
    ],
    [
      "47593/4",
      "10381023/8"
    ],
    [
      "22489/25",
      "1539388/125"
    ],
    [
      "229597/49",
      "109705616/343"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 249471 (Weierstrass model y^2 = x^3 - 432k^2, minimal model shown). Found in an exhaustive scan of cube-free k <= 7*10^5 by minimal-model naive height, with a Mestre-Nagao a_p sieve (p = 1 mod 3) and PARI ellrank 2-descent; companion to #5313 (k = 111690).",
  "created_at": "2026-10-21 13:09:28",
  "updated_at": "2026-10-21 13:09:28"
}