{
  "id": 6341,
  "curve_key": "0:40192462051848",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-46519053301"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 62.649401165646104,
  "faltings_height": 3.2784393395954705,
  "conductor": "15072173269443",
  "bad_primes": [
    "3",
    "271",
    "919"
  ],
  "discriminant": "-934857642239144411018643",
  "regulator": "40158.0972889270103026200820076312751606219925621",
  "points": [
    [
      "7657",
      "634356"
    ],
    [
      "249049/4",
      "124275447/8"
    ],
    [
      "7537177/1764",
      "13146643441/74088"
    ],
    [
      "19674871/1681",
      "85995215470/68921"
    ],
    [
      "24106199857/4669921",
      "3044779810885251/10091699281"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Published-source replay from OEIS A359687: k=2241441 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 −3^5·271^4·919^4 and the conductor is 15072173269443. Since c4=0 and 2c6=8965764², ICARM classifies this as a cube-sum curve. This is a published construction replay, not an original discovery.",
  "created_at": "2026-11-01 02:47:34",
  "updated_at": "2026-11-01 02:47:34"
}