{
  "id": 3318,
  "curve_key": "191961:-84104541",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-3999",
    "98343"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6
  ],
  "naive_height": 36.49514251613172,
  "faltings_height": 0.5645013480767915,
  "conductor": "1170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13"
  ],
  "discriminant": "1140750",
  "regulator": "2.683624853472045407371643724068477971489",
  "points": [
    [
      "67",
      "324"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1170b2 = LMFDB 1170.c2: https://www.lmfdb.org/EllipticCurve/Q/1170/c/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 1170, minimal discriminant 1140750, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:56:56",
  "updated_at": "2026-09-26 20:56:56"
}