{
  "id": 893,
  "curve_key": "193:575",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4",
    "-1"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    4,
    2
  ],
  "naive_height": 15.788070566714657,
  "faltings_height": -0.6189417971690055,
  "conductor": "21",
  "bad_primes": [
    "3",
    "7"
  ],
  "discriminant": "3969",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 21a1 = LMFDB 21.a5: https://www.lmfdb.org/EllipticCurve/Q/21/a/5\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 21, minimal discriminant 3969, torsion ℤ/2ℤ × ℤ/4ℤ.",
  "created_at": "2026-09-23 14:56:06",
  "updated_at": "2026-09-23 14:56:06"
}