{
  "id": 5661,
  "curve_key": "0:1937157768",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-2242081"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 42.76897533543771,
  "faltings_height": 1.6217371870781045,
  "conductor": "726434163",
  "bad_primes": [
    "3",
    "7",
    "13",
    "19"
  ],
  "discriminant": "-2171632070672883",
  "regulator": "17.708925708487128751776629455237749627179572",
  "points": [
    [
      "133",
      "332"
    ],
    [
      "247",
      "3581"
    ],
    [
      "1183/9",
      "4582/27"
    ]
  ],
  "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 = 15561 gives the global minimal model Y^2 + Y = X^3 - 2242081.\r\n\r\nThe explicit map is u = (A + 6Y + 3)/(6X) and v = (A - 6Y - 3)/(6X), with A = 15561. The three submitted points correspond to (u,v) = (22,17), (25,-4), and (820/39,719/39).\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 726434163.",
  "created_at": "2026-10-24 00:56:18",
  "updated_at": "2026-10-24 00:56:18"
}