{
  "id": 3290,
  "curve_key": "9821953:-30781996001",
  "ainvs": [
    "1",
    "1",
    "1",
    "-204624",
    "35542050"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 48.30039162118123,
  "faltings_height": 1.290661783231942,
  "conductor": "609",
  "bad_primes": [
    "3",
    "7",
    "29"
  ],
  "discriminant": "38367",
  "regulator": "7.026920478164243935451002467228854851369",
  "points": [
    [
      "1317",
      "44646"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 609b4 = LMFDB 609.a1: https://www.lmfdb.org/EllipticCurve/Q/609/a/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 609, minimal discriminant 38367, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:52:25",
  "updated_at": "2026-09-26 20:52:25"
}