{
  "id": 3333,
  "curve_key": "192:-3456",
  "ainvs": [
    "0",
    "0",
    "0",
    "-4",
    "4"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "naive_height": 16.295734259847894,
  "faltings_height": -0.629211884724564,
  "conductor": "88",
  "bad_primes": [
    "2",
    "11"
  ],
  "discriminant": "-2816",
  "regulator": "0.04026436433688064294321515224808125270452",
  "points": [
    [
      "2",
      "2"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 88a1 = LMFDB 88.a1: https://www.lmfdb.org/EllipticCurve/Q/88/a/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 88, minimal discriminant -2816, torsion trivial. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:59:21",
  "updated_at": "2026-09-26 20:59:21"
}