{
  "id": 6339,
  "curve_key": "0:1611722114173728",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-1865419113627"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 70.03215927677337,
  "faltings_height": 3.8936691821894094,
  "conductor": "7461676454508",
  "bad_primes": [
    "2",
    "3",
    "31",
    "61",
    "139"
  ],
  "discriminant": "-1503268618817495089625095728",
  "regulator": "1021.61637787099644346254421151616854584828206269",
  "points": [
    [
      "12927",
      "542934"
    ],
    [
      "788547",
      "700229736"
    ],
    [
      "924211",
      "888497452"
    ],
    [
      "788547/49",
      "520441020/343"
    ],
    [
      "10251111/25",
      "32820903234/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Published-source replay from OEIS A359687: k=525698 in the rank-5 sequence for y² = x³ − 432k². PARI/GP 2.17.4 returned exact rank bounds [5,5] with trivial torsion. The five displayed points were checked on the model. The discriminant factors as −2^4·3^9·31^4·61^4·139^4 and the conductor is 7461676454508. Since c4=0 and 2c6=56775384², ICARM classifies this as a cube-sum curve. This is a published construction replay, not an original discovery.",
  "created_at": "2026-11-01 02:43:44",
  "updated_at": "2026-11-01 02:43:44"
}