{
  "id": 5660,
  "curve_key": "0:1252000800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-1449075"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 41.8960174972035,
  "faltings_height": 1.548990700558587,
  "conductor": "469500300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "139"
  ],
  "discriminant": "-907121529630000",
  "regulator": "130.36723442643807921179283103844646962321315",
  "points": [
    [
      "139",
      "1112"
    ],
    [
      "15151/121",
      "954374/1331"
    ],
    [
      "402961/3364",
      "101328359/195112"
    ]
  ],
  "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 = 12510 gives the global minimal model Y^2 = X^3 - 1449075.\r\n\r\nThe explicit map is u = (A + 6Y)/(6X) and v = (A - 6Y)/(6X), with A = 12510. The three submitted points correspond to (u,v) = (23,7), (26831/1199,13099/1199), and (3655661/168142,2197699/168142).\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 469500300.",
  "created_at": "2026-10-24 00:55:04",
  "updated_at": "2026-10-24 00:55:04"
}