{
  "id": 3266,
  "curve_key": "75073:19567135",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1564",
    "-23299"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 33.678648757410116,
  "faltings_height": 0.7447825041337065,
  "conductor": "1122",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17"
  ],
  "discriminant": "23284318464",
  "regulator": "1.893763184624783638839174408974854649556",
  "points": [
    [
      "47",
      "75"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1122e2 = LMFDB 1122.e4: https://www.lmfdb.org/EllipticCurve/Q/1122/e/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 1122, minimal discriminant 23284318464, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:48:31",
  "updated_at": "2026-09-26 20:48:31"
}