{
  "id": 875,
  "curve_key": "-32:224",
  "ainvs": [
    "0",
    "1",
    "0",
    "1",
    "0"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2
  ],
  "naive_height": 10.823292103710079,
  "faltings_height": -0.9919258763598299,
  "conductor": "48",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "-48",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "LMFDB 48.a5 (Cremona 48a4): https://www.lmfdb.org/EllipticCurve/Q/48/a/5\n\nMordell–Weil rank exactly 0 per LMFDB. Conductor 48, minimal discriminant -48, 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 Faltings height.",
  "created_at": "2026-09-23 14:41:28",
  "updated_at": "2026-09-23 14:41:28"
}