{
  "id": 6330,
  "curve_key": "0:129432867267398712085630922356964167200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-149806559337267027876887641616856675"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 175.51245139006045,
  "faltings_height": 12.683693524963333,
  "conductor": "599226237349068111507550566467426700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "41",
    "53",
    "67",
    "79",
    "107",
    "139"
  ],
  "discriminant": "-9694946255243086195719670598429791581312398577875994469918827236568030000",
  "regulator": "875022017224.99073826912362935815536125147253362333375285",
  "points": [
    [
      "656685480091",
      "-365211913819642336"
    ],
    [
      "4485758554489/4",
      "-8981923377127388563/8"
    ],
    [
      "1209639441739",
      "1272859470827110412"
    ],
    [
      "10351308636769/16",
      "22260521432745447697/64"
    ],
    [
      "3815433394711",
      "-7442680104497489734"
    ],
    [
      "23587831475209/36",
      "78323428835974368773/216"
    ],
    [
      "95255281602079/25",
      "-928420492881041454358/125"
    ],
    [
      "2905537525616881/1444",
      "155170618028993633494121/54872"
    ],
    [
      "3590916849276409/6400",
      "83862069487568114520077/512000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = k with k = 148975046052222390 = 2*3*5*7*11*13*29*41*53*67*79*107*139 (model y^2 = x^3 - 432k^2, minimized). This k is N. Rogers's 2003 rank-9 example, cited in OEIS A060748 (https://oeis.org/A060748). Nine independent points were obtained from solutions of uv(u+v) = k*c^3 on the 3-isogenous curve y^2 = x^3 + 16k^2 and mapped across by the 3-isogeny; independence certified by reduction mod 2 and mod 5 at 80 good primes each, with trivial torsion.",
  "created_at": "2026-11-01 01:26:32",
  "updated_at": "2026-11-01 01:26:32"
}