{
  "id": 3289,
  "curve_key": "25873:-4161689",
  "ainvs": [
    "1",
    "1",
    "1",
    "-539",
    "4592"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 30.482865698682875,
  "faltings_height": 0.1154351744229599,
  "conductor": "663",
  "bad_primes": [
    "3",
    "13",
    "17"
  ],
  "discriminant": "25857",
  "regulator": "1.487906035555416466554332154999230916193",
  "points": [
    [
      "9",
      "19"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 663b1 = LMFDB 663.a4: https://www.lmfdb.org/EllipticCurve/Q/663/a/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 663, minimal discriminant 25857, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:52:15",
  "updated_at": "2026-09-26 20:52:15"
}