{
  "id": 947,
  "curve_key": "657:-22329",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-14",
    "29"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    9
  ],
  "naive_height": 20.02728312205604,
  "faltings_height": -0.31520442809991117,
  "conductor": "54",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "-124416",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 54b3 = LMFDB 54.b2: https://www.lmfdb.org/EllipticCurve/Q/54/b/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 54, minimal discriminant -124416, torsion ℤ/9ℤ.",
  "created_at": "2026-09-23 15:04:40",
  "updated_at": "2026-09-23 15:04:40"
}