{
  "id": 1180,
  "curve_key": "85681:-168541129",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1785",
    "194922"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    8
  ],
  "naive_height": 37.885380733985166,
  "faltings_height": 1.214635037094115,
  "conductor": "1785",
  "bad_primes": [
    "3",
    "5",
    "7",
    "17"
  ],
  "discriminant": "-16074715228425",
  "regulator": "2.023651471250951911811702097942194471646",
  "points": [
    [
      "63",
      "546"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1785o4, rank exactly 1 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.00000-09999 . Found by screening the local allgens tables for missing torsion size records; torsion and independence independently verified by the site.",
  "created_at": "2026-09-23 21:38:33",
  "updated_at": "2026-09-23 21:38:33"
}