{
  "id": 1154,
  "curve_key": "168777:-69324741",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-3516",
    "81116"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "naive_height": 36.10900078780843,
  "faltings_height": 0.7248747728745522,
  "conductor": "201042",
  "bad_primes": [
    "2",
    "3",
    "17",
    "73"
  ],
  "discriminant": "1045820484",
  "regulator": "3.5650006521571686183568398472462834100617117",
  "points": [
    [
      "34",
      "-14"
    ],
    [
      "31",
      "19"
    ],
    [
      "35",
      "-21"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 201042o1, rank exactly 3 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.200000-209999 . 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 21:37:47",
  "updated_at": "2026-09-23 21:37:47"
}