{
  "id": 1148,
  "curve_key": "112:-1504",
  "ainvs": [
    "0",
    "1",
    "0",
    "-2",
    "1"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "naive_height": 14.63176700901957,
  "faltings_height": -0.7717616044269274,
  "conductor": "124",
  "bad_primes": [
    "2",
    "31"
  ],
  "discriminant": "-496",
  "regulator": "0.5205306938826742774502387930373645426292",
  "points": [
    [
      "2",
      "3"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 124a1, 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 21:37:36",
  "updated_at": "2026-09-23 21:37:36"
}