{
  "id": 1016,
  "curve_key": "-63:-513",
  "ainvs": [
    "1",
    "-1",
    "1",
    "1",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "naive_height": 12.480551690341539,
  "faltings_height": -0.839281637588401,
  "conductor": "297",
  "bad_primes": [
    "3",
    "11"
  ],
  "discriminant": "-297",
  "regulator": "0.3146944998668636367163098982530917719998",
  "points": [
    [
      "0",
      "0"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 297b1 = LMFDB 297.b1: https://www.lmfdb.org/EllipticCurve/Q/297/b/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 297, minimal discriminant -297, trivial torsion. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:16:28",
  "updated_at": "2026-09-23 15:16:28"
}