{
  "id": 656,
  "curve_key": "16:-1880",
  "ainvs": [
    "0",
    "-1",
    "1",
    "0",
    "2"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "naive_height": 15.07805411164799,
  "faltings_height": -0.6857169663237132,
  "conductor": "681",
  "bad_primes": [
    "3",
    "227"
  ],
  "discriminant": "-2043",
  "regulator": "0.136079688950694268446478372652388595164331",
  "points": [
    [
      "0",
      "1"
    ],
    [
      "3",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 681c1 = LMFDB 681.a1. Curve data, generators (0, 1) and (3, 4) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/681/a/1",
  "created_at": "2026-09-08 19:03:56",
  "updated_at": "2026-09-08 19:03:56"
}