{
  "id": 3249,
  "curve_key": "4032:-272376",
  "ainvs": [
    "0",
    "0",
    "1",
    "-84",
    "315"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "naive_height": 25.02987748729817,
  "faltings_height": 0.0334391569913178,
  "conductor": "171",
  "bad_primes": [
    "3",
    "19"
  ],
  "discriminant": "-5000211",
  "regulator": "0.6779006064770846362536787946564408518636",
  "points": [
    [
      "5",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 171b2 = LMFDB 171.b2: https://www.lmfdb.org/EllipticCurve/Q/171/b/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 171, minimal discriminant -5000211, torsion ℤ/3ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:45:44",
  "updated_at": "2026-09-26 20:45:44"
}