{
  "id": 3265,
  "curve_key": "1331728:-1536758720",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-27744",
    "1787904"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 42.30596371507725,
  "faltings_height": 1.193651875921445,
  "conductor": "816",
  "bad_primes": [
    "2",
    "3",
    "17"
  ],
  "discriminant": "110841053184",
  "regulator": "3.826981769488477113371502881457380599672",
  "points": [
    [
      "146",
      "910"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 816h3 = LMFDB 816.b2: https://www.lmfdb.org/EllipticCurve/Q/816/b/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 816, minimal discriminant 110841053184, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:48:22",
  "updated_at": "2026-09-26 20:48:22"
}