{
  "id": 868,
  "curve_key": "33:-81",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1",
    "0"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    4
  ],
  "naive_height": 10.489522684399441,
  "faltings_height": -1.0697833015012888,
  "conductor": "17",
  "bad_primes": [
    "17"
  ],
  "discriminant": "17",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "LMFDB 17.a4 (Cremona 17a4): https://www.lmfdb.org/EllipticCurve/Q/17/a/4\n\nMordell–Weil rank exactly 0 per LMFDB. Conductor 17, minimal discriminant 17, 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): #3 by Faltings height, #6 by |minimal discriminant|.",
  "created_at": "2026-09-23 14:40:24",
  "updated_at": "2026-09-23 14:40:24"
}