{
  "id": 5327,
  "curve_key": "0:2429028405000",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-2811375469"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 57.037024919986024,
  "faltings_height": 2.8107413191237973,
  "conductor": "36435426075",
  "bad_primes": [
    "3",
    "5",
    "31",
    "79"
  ],
  "discriminant": "-3414455435356969921875",
  "regulator": "570.0801518717026798241240960197071537284228203",
  "points": [
    [
      "1519",
      "26334"
    ],
    [
      "2449",
      "108980"
    ],
    [
      "8029",
      "717479"
    ],
    [
      "193471/9",
      "85086818/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 551025 (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 13:10:06",
  "updated_at": "2026-10-21 13:10:06"
}