{
  "id": 3185,
  "curve_key": "-63:1215",
  "ainvs": [
    "1",
    "-1",
    "1",
    "1",
    "-2"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 14.204998711549297,
  "faltings_height": -0.7417480411904633,
  "conductor": "333",
  "bad_primes": [
    "3",
    "37"
  ],
  "discriminant": "-999",
  "regulator": "0.9605876837473819112921810576819444984411",
  "points": [
    [
      "2",
      "1"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 333c1 = LMFDB 333.a2: https://www.lmfdb.org/EllipticCurve/Q/333/a/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 333, minimal discriminant -999, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:41:37",
  "updated_at": "2026-09-26 20:41:37"
}