{
  "id": 867,
  "curve_key": "1:-161",
  "ainvs": [
    "1",
    "1",
    "1",
    "0",
    "0"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    4
  ],
  "naive_height": 10.162808729968926,
  "faltings_height": -1.0954247526427892,
  "conductor": "15",
  "bad_primes": [
    "3",
    "5"
  ],
  "discriminant": "-15",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "LMFDB 15.a7 (Cremona 15a8): https://www.lmfdb.org/EllipticCurve/Q/15/a/7\n\nMordell–Weil rank exactly 0 per LMFDB. Conductor 15, minimal discriminant -15, torsion ℤ/4ℤ.\n\nSubmitted as one of the ten smallest rank-0 curves in LMFDB (as of 2026-09-23; places in LMFDB sort order, ties broken by label): #2 by Faltings height, #4 by |minimal discriminant|.",
  "created_at": "2026-09-23 14:40:23",
  "updated_at": "2026-09-23 14:40:23"
}