{
  "id": 953,
  "curve_key": "-944:33128",
  "ainvs": [
    "0",
    "1",
    "1",
    "20",
    "-32"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    5
  ],
  "naive_height": 20.816268250450808,
  "faltings_height": -0.1533117049886217,
  "conductor": "57",
  "bad_primes": [
    "3",
    "19"
  ],
  "discriminant": "-1121931",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 57c1 = LMFDB 57.b2: https://www.lmfdb.org/EllipticCurve/Q/57/b/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 57, minimal discriminant -1121931, torsion ℤ/5ℤ.",
  "created_at": "2026-09-23 15:05:44",
  "updated_at": "2026-09-23 15:05:44"
}