{
  "id": 1001,
  "curve_key": "-719:-6697",
  "ainvs": [
    "1",
    "0",
    "0",
    "15",
    "9"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    5
  ],
  "naive_height": 19.73358407316314,
  "faltings_height": -0.27837864612393415,
  "conductor": "186",
  "bad_primes": [
    "2",
    "3",
    "31"
  ],
  "discriminant": "-241056",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 186b1 = LMFDB 186.c2: https://www.lmfdb.org/EllipticCurve/Q/186/c/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 186, minimal discriminant -241056, torsion ℤ/5ℤ.",
  "created_at": "2026-09-23 15:13:17",
  "updated_at": "2026-09-23 15:13:17"
}