{
  "id": 866,
  "curve_key": "103681:33384799",
  "ainvs": [
    "1",
    "1",
    "1",
    "-2160",
    "-39540"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2
  ],
  "naive_height": 34.64722246980395,
  "faltings_height": 0.2908696084771015,
  "conductor": "15",
  "bad_primes": [
    "3",
    "5"
  ],
  "discriminant": "405",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "LMFDB 15.a1 (Cremona 15a5): https://www.lmfdb.org/EllipticCurve/Q/15/a/1\n\nMordell–Weil rank exactly 0 per LMFDB. Conductor 15, minimal discriminant 405, torsion ℤ/2ℤ.\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): #10 by conductor.",
  "created_at": "2026-09-23 14:40:23",
  "updated_at": "2026-09-23 14:40:23"
}