{
  "id": 5606,
  "curve_key": "257866181269551936:-136741296859641068622114816",
  "ainvs": [
    "0",
    "0",
    "0",
    "-5372212109782332",
    "158265389883843829423744"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 120.36026605685123,
  "faltings_height": 7.9608879625632545,
  "conductor": "5585900418520662240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "37",
    "107",
    "2213",
    "19231"
  ],
  "discriminant": "-897788737734458824321263883512358475342400000000",
  "regulator": "9056.726461884592206425345404632975817351509876880915",
  "points": [
    [
      "46282058",
      "93626186940"
    ],
    [
      "57333098",
      "196770279420"
    ],
    [
      "61777538",
      "249309274500"
    ],
    [
      "66319658",
      "306064822140"
    ],
    [
      "104063210",
      "852133814532"
    ],
    [
      "234396413",
      "3431788234875"
    ],
    [
      "308114288",
      "5268174219000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained in my own run by specializing the Khoshnam–Moody four-section family with rational torsion Z/4Z at (c,d,m,n) = (3/11,1/11,1,1).\r\n\r\nSource: Sections 2–3, equations (2.1)–(3.3):\r\nhttps://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=922952\r\n\r\nThe four specialized sections seeded the point search. Seven independent rational points were obtained and transported to the global minimal model [0,0,0,-5372212109782332,158265389883843829423744]. All seven points were checked exactly on this model. The computation returned matching rank bounds [7,7], establishing rank exactly 7, with rational torsion Z/4Z and conductor 5585900418520662240.",
  "created_at": "2026-10-23 22:27:30",
  "updated_at": "2026-10-23 22:27:30"
}