{
  "id": 2922,
  "curve_key": "3265:-114625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-68",
    "127"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 24.273045125131596,
  "faltings_height": 0.06272695766947857,
  "conductor": "227975",
  "bad_primes": [
    "5",
    "11",
    "829"
  ],
  "discriminant": "12538625",
  "regulator": "4.5407341717788111949252616043091469156426614",
  "points": [
    [
      "7",
      "-1"
    ],
    [
      "-3",
      "19"
    ],
    [
      "-7",
      "20"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 227975a1 = LMFDB 227975.a1: https://www.lmfdb.org/EllipticCurve/Q/227975/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 227975, minimal discriminant 12538625, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:28:30",
  "updated_at": "2026-09-26 20:28:30"
}