{
  "id": 896,
  "curve_key": "-47:71",
  "ainvs": [
    "1",
    "0",
    "0",
    "1",
    "0"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    4
  ],
  "naive_height": 11.550442805130176,
  "faltings_height": -0.9655153874489782,
  "conductor": "21",
  "bad_primes": [
    "3",
    "7"
  ],
  "discriminant": "-63",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 21a4 = LMFDB 21.a6: https://www.lmfdb.org/EllipticCurve/Q/21/a/6\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 21, minimal discriminant -63, torsion ℤ/4ℤ.",
  "created_at": "2026-09-23 14:57:09",
  "updated_at": "2026-09-23 14:57:09"
}