{
  "id": 3106,
  "curve_key": "9513:-924885",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-198",
    "1120"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 27.481243689619372,
  "faltings_height": 0.10777865320341132,
  "conductor": "198",
  "bad_primes": [
    "2",
    "3",
    "11"
  ],
  "discriminant": "3175524",
  "regulator": "0.3900859827946226837772726842820017242934",
  "points": [
    [
      "6",
      "8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 198a2 = LMFDB 198.a2: https://www.lmfdb.org/EllipticCurve/Q/198/a/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 198, minimal discriminant 3175524, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:37:33",
  "updated_at": "2026-09-26 20:37:33"
}