{
  "id": 651,
  "curve_key": "721:-19385",
  "ainvs": [
    "1",
    "1",
    "1",
    "-15",
    "16"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "naive_height": 19.74450970021006,
  "faltings_height": -0.5716798947412859,
  "conductor": "563",
  "bad_primes": [
    "563"
  ],
  "discriminant": "-563",
  "regulator": "0.219229003517995456286946191043342445936013",
  "points": [
    [
      "2",
      "-2"
    ],
    [
      "4",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 563a1 = LMFDB 563.a1. Curve data, generators (2, -2) and (4, 4) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/563/a/1",
  "created_at": "2026-09-08 19:03:37",
  "updated_at": "2026-09-08 19:03:37"
}