{
  "id": 878,
  "curve_key": "36928:7096328",
  "ainvs": [
    "0",
    "1",
    "1",
    "-769",
    "-8470"
  ],
  "rank_lower_bound": 0,
  "torsion": [],
  "naive_height": 31.55017605025529,
  "faltings_height": 0.0334391569913178,
  "conductor": "19",
  "bad_primes": [
    "19"
  ],
  "discriminant": "-19",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "LMFDB 19.a1 (Cremona 19a2): https://www.lmfdb.org/EllipticCurve/Q/19/a/1\n\nMordell–Weil rank exactly 0 per LMFDB. Conductor 19, minimal discriminant -19, torsion trivial.\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): #7 by |minimal discriminant|.",
  "created_at": "2026-09-23 14:41:30",
  "updated_at": "2026-09-23 14:41:30"
}