{
  "id": 974,
  "curve_key": "49:-521",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "naive_height": 12.511500083506734,
  "faltings_height": -0.9268756267283376,
  "conductor": "89",
  "bad_primes": [
    "89"
  ],
  "discriminant": "-89",
  "regulator": "0.1121048812300989494200897750437008367331",
  "points": [
    [
      "0",
      "0"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 89a1 = LMFDB 89.a1: https://www.lmfdb.org/EllipticCurve/Q/89/a/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 89, minimal discriminant -89, trivial torsion. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:08:58",
  "updated_at": "2026-09-23 15:08:58"
}