{
  "id": 3205,
  "curve_key": "208:2944",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-4",
    "-2"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 16.012614239103954,
  "faltings_height": -0.7727939607831388,
  "conductor": "192",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "192",
  "regulator": "1.351603734412083332293812071952292680515",
  "points": [
    [
      "3",
      "2"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 192a1 = LMFDB 192.a3: https://www.lmfdb.org/EllipticCurve/Q/192/a/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 192, minimal discriminant 192, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:42:36",
  "updated_at": "2026-09-26 20:42:36"
}