{
  "id": 5657,
  "curve_key": "0:198164232",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-229357"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 38.209213398793885,
  "faltings_height": 1.2417570256911195,
  "conductor": "74311587",
  "bad_primes": [
    "3",
    "7",
    "79"
  ],
  "discriminant": "-22725152108883",
  "regulator": "24.301536406957691471083059167426027958483674",
  "points": [
    [
      "79",
      "513"
    ],
    [
      "553",
      "12995"
    ],
    [
      "10033/121",
      "776260/1331"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Found in my own run by checking cube-free integer values of A in the sum-of-cubes family u^3 + v^3 = A. The specialization A = 4977 gives the global minimal model Y^2 + Y = X^3 - 229357.\r\n\r\nThe explicit map is u = (A + 6Y + 3)/(6X) and v = (A - 6Y - 3)/(6X), with A = 4977. The three submitted points correspond to (u,v) = (17,4), (25,-22), and (23810/1397,4141/1397).\r\n\r\nAll three points were checked exactly and are independent. Matching rank bounds [3,3] establish rank exactly 3, with trivial rational torsion and conductor 74311587.",
  "created_at": "2026-10-24 00:50:48",
  "updated_at": "2026-10-24 00:50:48"
}