{
  "id": 939,
  "curve_key": "208:2240",
  "ainvs": [
    "0",
    "1",
    "0",
    "-4",
    "-4"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2,
    2
  ],
  "naive_height": 16.012614239103954,
  "faltings_height": -0.6453522860798573,
  "conductor": "48",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "2304",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 48a1 = LMFDB 48.a4: https://www.lmfdb.org/EllipticCurve/Q/48/a/4\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 48, minimal discriminant 2304, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-23 15:03:36",
  "updated_at": "2026-09-23 15:03:36"
}