{
  "id": 3335,
  "curve_key": "88060325089293998722576:-57145975579024392221992935316892224",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1834590106026958306720",
    "66141175438074109110482837181200"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 160.06183407600014,
  "faltings_height": 11.386472908226155,
  "conductor": "1185557421935264818440",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "31",
    "67",
    "89",
    "193",
    "347",
    "2039"
  ],
  "discriminant": "-1494669034408399803847005284005580359490923482072604670593193702400",
  "regulator": "7534307.037734179442494821425851534602589587876112350",
  "points": [
    [
      "42061619504",
      "7961778288852420"
    ],
    [
      "45860199379",
      "8857637801700870"
    ],
    [
      "777830275360/81",
      "5124274585669179460/729"
    ],
    [
      "-24724908877",
      "9817657035952194"
    ],
    [
      "-3455199993097/361",
      "62422022620480451604/6859"
    ],
    [
      "1634347500896/25",
      "1877491518420156756/125"
    ],
    [
      "119853220791440/5329",
      "2342400848500524387420/389017"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1830 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 7 carries over. Torsion ℤ/4ℤ.",
  "created_at": "2026-09-26 21:01:44",
  "updated_at": "2026-09-26 21:01:44"
}