{
  "id": 898,
  "curve_key": "1633:185039",
  "ainvs": [
    "1",
    "0",
    "0",
    "-34",
    "-217"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2
  ],
  "naive_height": 24.256643785307592,
  "faltings_height": 0.07420538339093977,
  "conductor": "21",
  "bad_primes": [
    "3",
    "7"
  ],
  "discriminant": "-17294403",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 21a6 = LMFDB 21.a4: https://www.lmfdb.org/EllipticCurve/Q/21/a/4\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 21, minimal discriminant -17294403, torsion ℤ/2ℤ.",
  "created_at": "2026-09-23 14:57:10",
  "updated_at": "2026-09-23 14:57:10"
}