{
  "id": 944,
  "curve_key": "-32:872",
  "ainvs": [
    "0",
    "1",
    "1",
    "1",
    "-1"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    3
  ],
  "naive_height": 13.54157884781796,
  "faltings_height": -0.808529717074587,
  "conductor": "51",
  "bad_primes": [
    "3",
    "17"
  ],
  "discriminant": "-459",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 51a1 = LMFDB 51.a2: https://www.lmfdb.org/EllipticCurve/Q/51/a/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 51, minimal discriminant -459, torsion ℤ/3ℤ.",
  "created_at": "2026-09-23 15:04:39",
  "updated_at": "2026-09-23 15:04:39"
}