{
  "id": 3254,
  "curve_key": "-3920:361376",
  "ainvs": [
    "0",
    "1",
    "0",
    "82",
    "-391"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    3
  ],
  "naive_height": 25.595348493046792,
  "faltings_height": 0.22805768159771145,
  "conductor": "32828",
  "bad_primes": [
    "2",
    "29",
    "283"
  ],
  "discriminant": "-110433392",
  "regulator": "9.37595281834571421851847186027113026390392",
  "points": [
    [
      "5",
      "13"
    ],
    [
      "98",
      "979"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 32828a1 = LMFDB 32828.a2: https://www.lmfdb.org/EllipticCurve/Q/32828/a/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 32828, minimal discriminant -110433392, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:46:32",
  "updated_at": "2026-09-26 20:46:32"
}