{
  "id": 876,
  "curve_key": "3841:-238049",
  "ainvs": [
    "1",
    "1",
    "1",
    "-80",
    "242"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    4
  ],
  "naive_height": 24.760464085037714,
  "faltings_height": -0.4022775720828438,
  "conductor": "15",
  "bad_primes": [
    "3",
    "5"
  ],
  "discriminant": "15",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "LMFDB 15.a4 (Cremona 15a7): https://www.lmfdb.org/EllipticCurve/Q/15/a/4\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): #3 by |minimal discriminant|.",
  "created_at": "2026-09-23 14:41:29",
  "updated_at": "2026-09-23 14:41:29"
}