{
  "id": 1174,
  "curve_key": "1561:-61309",
  "ainvs": [
    "1",
    "0",
    "1",
    "-33",
    "68"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6
  ],
  "naive_height": 22.059245761546297,
  "faltings_height": -0.31885674185639123,
  "conductor": "130",
  "bad_primes": [
    "2",
    "5",
    "13"
  ],
  "discriminant": "26000",
  "regulator": "1.170464153594722231116300800325189639761",
  "points": [
    [
      "2",
      "2"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 130a1, 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 21:38:19",
  "updated_at": "2026-09-23 21:38:19"
}