{
  "id": 655,
  "curve_key": "336:-8640",
  "ainvs": [
    "0",
    "0",
    "0",
    "-7",
    "10"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "naive_height": 18.128315723596202,
  "faltings_height": -0.46638702605939963,
  "conductor": "664",
  "bad_primes": [
    "2",
    "83"
  ],
  "discriminant": "-21248",
  "regulator": "0.0966760504530515052579053796496668914274579",
  "points": [
    [
      "1",
      "2"
    ],
    [
      "3",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 664a1 = LMFDB 664.a1. Curve data, generators (1, 2) and (3, 4) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/664/a/1",
  "created_at": "2026-09-08 19:03:52",
  "updated_at": "2026-09-08 19:03:52"
}