{
  "id": 917,
  "curve_key": "553:-4085",
  "ainvs": [
    "1",
    "1",
    "0",
    "-11",
    "0"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2,
    2
  ],
  "naive_height": 18.946074004567006,
  "faltings_height": -0.35920565739666127,
  "conductor": "33",
  "bad_primes": [
    "3",
    "11"
  ],
  "discriminant": "88209",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 33a1 = LMFDB 33.a2: https://www.lmfdb.org/EllipticCurve/Q/33/a/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 33, minimal discriminant 88209, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-23 15:00:23",
  "updated_at": "2026-09-23 15:00:23"
}