{
  "id": 1155,
  "curve_key": "1041:-33561",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-22",
    "44"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 20.843811205844908,
  "faltings_height": -0.4983375074679089,
  "conductor": "205",
  "bad_primes": [
    "5",
    "41"
  ],
  "discriminant": "1025",
  "regulator": "1.602601397324700955066904509537931569839",
  "points": [
    [
      "-1",
      "8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 205a1, 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 21:37:49",
  "updated_at": "2026-09-23 21:37:49"
}