{
  "id": 642,
  "curve_key": "112:-1304",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-2",
    "2"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "naive_height": 14.346383484973197,
  "faltings_height": -0.8365484092785727,
  "conductor": "57",
  "bad_primes": [
    "3",
    "19"
  ],
  "discriminant": "-171",
  "regulator": "0.03757459273682375282480511121671040840484",
  "points": [
    [
      "2",
      "1"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 57a1 = LMFDB 57.a1, the rank-1 curve of smallest conductor not previously on the board. Curve data, generator (2, 1) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/57/a/1",
  "created_at": "2026-09-08 17:17:39",
  "updated_at": "2026-09-08 17:17:39"
}