{
  "id": 5655,
  "curve_key": "0:53003808",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-61347"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 35.57174863598396,
  "faltings_height": 1.0219682954569587,
  "conductor": "19876428",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13"
  ],
  "discriminant": "-1625812304688",
  "regulator": "46.770100414791036452634329026253428336970081",
  "points": [
    [
      "91",
      "832"
    ],
    [
      "247",
      "3874"
    ],
    [
      "793/4",
      "22243/8"
    ]
  ],
  "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 = 2574 gives the global minimal model Y^2 = X^3 - 61347.\r\n\r\nThe explicit map is u = (A + 6Y)/(6X) and v = (A - 6Y)/(6X), with A = 2574. The three submitted points correspond to (u,v) = (97/7,-31/7), (331/19,-265/19), and (1975/122,-1447/122).\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 19876428.",
  "created_at": "2026-10-24 00:47:16",
  "updated_at": "2026-10-24 00:47:16"
}