{
  "id": 1129,
  "curve_key": "2041:-15245",
  "ainvs": [
    "1",
    "1",
    "0",
    "-42",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 22.863585488429536,
  "faltings_height": -0.028142601144212773,
  "conductor": "113946",
  "bad_primes": [
    "2",
    "3",
    "7",
    "2713"
  ],
  "discriminant": "4785732",
  "regulator": "1.9255937080775220743267207961480461492800741",
  "points": [
    [
      "6",
      "0"
    ],
    [
      "7",
      "7"
    ],
    [
      "-3",
      "-9"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 113946b1, rank exactly 3 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.110000-119999 . 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 21:36:57",
  "updated_at": "2026-09-23 21:36:57"
}