{
  "id": 895,
  "curve_key": "1873:-80569",
  "ainvs": [
    "1",
    "0",
    "0",
    "-39",
    "90"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    8
  ],
  "naive_height": 22.605890107332264,
  "faltings_height": -0.2723682068890329,
  "conductor": "21",
  "bad_primes": [
    "3",
    "7"
  ],
  "discriminant": "45927",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 21a3 = LMFDB 21.a3: https://www.lmfdb.org/EllipticCurve/Q/21/a/3\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 21, minimal discriminant 45927, torsion ℤ/8ℤ.",
  "created_at": "2026-09-23 14:57:08",
  "updated_at": "2026-09-23 14:57:08"
}