{
  "id": 6338,
  "curve_key": "0:7840942560648",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-9075165001"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 59.38076033527384,
  "faltings_height": 3.0060526037311153,
  "conductor": "36300660003",
  "bad_primes": [
    "3",
    "37",
    "991"
  ],
  "discriminant": "-35578923749641906920243",
  "regulator": "254.3589151102224944951405820947006842544230821",
  "points": [
    [
      "14097/4",
      "1490171/8"
    ],
    [
      "110001/16",
      "35970295/64"
    ],
    [
      "110001/25",
      "34485251/125"
    ],
    [
      "476671/25",
      "328884594/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Published-source replay from OEIS A309964: k=36667 in the rank-4 sequence for y² = x³ − 432k². The global minimal model is [0,0,1,0,−9075165001]. PARI/GP 2.17.4 returned exact rank bounds [4,4] with trivial torsion. All four displayed points were checked on this model. The discriminant factors as −3^9·37^4·991^4 and the conductor is 36300660003. Here c4=0 and 2c6=3960036², so ICARM classifies the curve as cube-sum. This is a published construction replay, not an original discovery.",
  "created_at": "2026-11-01 02:39:45",
  "updated_at": "2026-11-01 02:39:45"
}