{
  "id": 996,
  "curve_key": "64:136",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-1",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "naive_height": 12.476649250079015,
  "faltings_height": -0.8964709784051836,
  "conductor": "141",
  "bad_primes": [
    "3",
    "47"
  ],
  "discriminant": "141",
  "regulator": "0.1984952364630847608336826286203908894590",
  "points": [
    [
      "0",
      "0"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 141d1 = LMFDB 141.d1: https://www.lmfdb.org/EllipticCurve/Q/141/d/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 141, minimal discriminant 141, trivial torsion. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:12:13",
  "updated_at": "2026-09-23 15:12:13"
}