{
  "id": 3282,
  "curve_key": "9537:-397953",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-199",
    "510"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 27.488802748736738,
  "faltings_height": 0.3468233705268193,
  "conductor": "289",
  "bad_primes": [
    "17"
  ],
  "discriminant": "410338673",
  "regulator": "3.035256177730332160832053603271747336052",
  "points": [
    [
      "-12",
      "38"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 289a1 = LMFDB 289.a4: https://www.lmfdb.org/EllipticCurve/Q/289/a/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 289, minimal discriminant 410338673, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:51:06",
  "updated_at": "2026-09-26 20:51:06"
}