{
  "id": 3278,
  "curve_key": "6208:-488960",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-129",
    "609"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 26.200782185589166,
  "faltings_height": -0.07964678022319349,
  "conductor": "192",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "98304",
  "regulator": "1.351603734412083332293812071952292680515",
  "points": [
    [
      "8",
      "5"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 192a3 = LMFDB 192.a1: https://www.lmfdb.org/EllipticCurve/Q/192/a/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 192, minimal discriminant 98304, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:50:28",
  "updated_at": "2026-09-26 20:50:28"
}