{
  "id": 6340,
  "curve_key": "0:27032047882332192",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-31287092456403"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 75.67159903128295,
  "faltings_height": 4.363622495065208,
  "conductor": "125148369825612",
  "bad_primes": [
    "2",
    "3",
    "7",
    "61",
    "2521"
  ],
  "discriminant": "-422877090690220107652861712688",
  "regulator": "3217.80966220061222933101972170467727641090038409",
  "points": [
    [
      "370587",
      "225528660"
    ],
    [
      "3229401/4",
      "5803233597/8"
    ],
    [
      "3229401/64",
      "5047553763/512"
    ],
    [
      "36446097/1156",
      "8920066905/39304"
    ],
    [
      "255122679/625",
      "4074024996342/15625"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Published-source replay from OEIS A359687: k=2152934 in the rank-5 sequence for y² = x³ − 432k². PARI/GP 2.17.4 returned exact rank bounds [5,5] with trivial torsion. All five displayed points were checked on the model. The discriminant factors as −2^4·3^9·7^4·61^4·2521^4 and the conductor is 125148369825612. Since c4=0 and 2c6=232516872², ICARM classifies this as a cube-sum curve. This is a published construction replay, not an original discovery.",
  "created_at": "2026-11-01 02:45:28",
  "updated_at": "2026-11-01 02:45:28"
}