{
  "id": 425,
  "curve_key": "-15:-297",
  "ainvs": [
    "1",
    "-1",
    "1",
    "0",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "naive_height": 11.3874642776054,
  "faltings_height": -0.9885476880985635,
  "conductor": "53",
  "bad_primes": [
    "53"
  ],
  "discriminant": "-53",
  "regulator": "0.09298148463865430334804190550967810967388",
  "points": [
    [
      "0",
      "0"
    ]
  ],
  "submitter": "NDElkies",
  "history": [],
  "commentary": "\r\nThe third elliptic curve of positive rank (LMFDB 53.a1, also the Fricke quotient of the modular curve X_0(53)), which happens to have a somewhat smaller naive height than the rank-1 curve of conductor 37.",
  "created_at": "2026-08-29 17:27:26",
  "updated_at": "2026-08-29 17:27:26"
}