{
  "id": 2963,
  "curve_key": "613873:-480967145",
  "ainvs": [
    "1",
    "1",
    "1",
    "-12789",
    "551346"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 39.98263003603193,
  "faltings_height": 0.9440881929519693,
  "conductor": "609",
  "bad_primes": [
    "3",
    "7",
    "29"
  ],
  "discriminant": "1472026689",
  "regulator": "3.513460239082121967725501233614427425684",
  "points": [
    [
      "-104",
      "929"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 609b2 = LMFDB 609.a4: https://www.lmfdb.org/EllipticCurve/Q/609/a/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 609, minimal discriminant 1472026689, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:30:35",
  "updated_at": "2026-09-26 20:30:35"
}