{
  "id": 653,
  "curve_key": "193:-2881",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4",
    "3"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "naive_height": 15.931785470169057,
  "faltings_height": -0.7177348242809212,
  "conductor": "643",
  "bad_primes": [
    "643"
  ],
  "discriminant": "-643",
  "regulator": "0.229179621568847078938767135198384435021017",
  "points": [
    [
      "1",
      "0"
    ],
    [
      "2",
      "1"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 643a1 = LMFDB 643.a1. Curve data, generators (1, 0) and (2, 1) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/643/a/1",
  "created_at": "2026-09-08 19:03:43",
  "updated_at": "2026-09-08 19:03:43"
}