{
  "id": 980,
  "curve_key": "-48:-216",
  "ainvs": [
    "0",
    "0",
    "1",
    "1",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "naive_height": 11.613603032723672,
  "faltings_height": -0.9363294187881737,
  "conductor": "91",
  "bad_primes": [
    "7",
    "13"
  ],
  "discriminant": "-91",
  "regulator": "0.1423921506687686591847910949737051319662",
  "points": [
    [
      "0",
      "0"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 91a1 = LMFDB 91.a1: https://www.lmfdb.org/EllipticCurve/Q/91/a/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 91, minimal discriminant -91, trivial torsion. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:10:03",
  "updated_at": "2026-09-23 15:10:03"
}