{
  "id": 2944,
  "curve_key": "8281:-748765",
  "ainvs": [
    "1",
    "0",
    "1",
    "-173",
    "852"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 27.0651570391011,
  "faltings_height": 0.1013955294743535,
  "conductor": "189926",
  "bad_primes": [
    "2",
    "11",
    "89",
    "97"
  ],
  "discriminant": "4178372",
  "regulator": "2.8089144858378304944019278715238272391242215",
  "points": [
    [
      "9",
      "2"
    ],
    [
      "8",
      "-5"
    ],
    [
      "5",
      "8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 189926b1 = LMFDB 189926.a1: https://www.lmfdb.org/EllipticCurve/Q/189926/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 189926, minimal discriminant 4178372, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:29:27",
  "updated_at": "2026-09-26 20:29:27"
}