{
  "id": 2697,
  "curve_key": "26113:-4080545",
  "ainvs": [
    "1",
    "1",
    "1",
    "-544",
    "4496"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 30.5105656607975,
  "faltings_height": 0.46200876470293256,
  "conductor": "663",
  "bad_primes": [
    "3",
    "13",
    "17"
  ],
  "discriminant": "668584449",
  "regulator": "2.975812071110832933108664309998461832386",
  "points": [
    [
      "79",
      "640"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 663b2 = LMFDB 663.a3: https://www.lmfdb.org/EllipticCurve/Q/663/a/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 663, minimal discriminant 668584449, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:18:13",
  "updated_at": "2026-09-26 20:18:13"
}