{
  "id": 872,
  "curve_key": "-23:235",
  "ainvs": [
    "1",
    "1",
    "0",
    "1",
    "0"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2
  ],
  "naive_height": 10.919171028288318,
  "faltings_height": -1.0115136426883327,
  "conductor": "39",
  "bad_primes": [
    "3",
    "13"
  ],
  "discriminant": "-39",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "LMFDB 39.a4 (Cremona 39a4): https://www.lmfdb.org/EllipticCurve/Q/39/a/4\n\nMordell–Weil rank exactly 0 per LMFDB. Conductor 39, minimal discriminant -39, 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): #8 by Faltings height.",
  "created_at": "2026-09-23 14:40:26",
  "updated_at": "2026-09-23 14:40:26"
}