{
  "id": 5662,
  "curve_key": "0:2779298568",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-3216781"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 43.490928838286884,
  "faltings_height": 1.6818999789822024,
  "conductor": "1042236963",
  "bad_primes": [
    "3",
    "19",
    "109"
  ],
  "discriminant": "-4470197066022483",
  "regulator": "42.039064586624739732998421869020329901309926",
  "points": [
    [
      "2071",
      "94230"
    ],
    [
      "14497/16",
      "1741679/64"
    ],
    [
      "14497/9",
      "1744804/27"
    ]
  ],
  "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 = 18639 gives the global minimal model Y^2 + Y = X^3 - 3216781.\r\n\r\nThe explicit map is u = (A + 6Y + 3)/(6X) and v = (A - 6Y - 3)/(6X), with A = 18639. The three submitted points correspond to (u,v) = (47,-44), (937/28,-745/28), and (883/21,-802/21).\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 1042236963.",
  "created_at": "2026-10-24 00:57:25",
  "updated_at": "2026-10-24 00:57:25"
}