{
  "id": 2947,
  "curve_key": "0:-77976",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "90"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    3
  ],
  "naive_height": 22.52831273203409,
  "faltings_height": -0.06498469653886367,
  "conductor": "9747",
  "bad_primes": [
    "3",
    "19"
  ],
  "discriminant": "-3518667",
  "regulator": "7.19459159982179587326343538683724463630458",
  "points": [
    [
      "6",
      "17"
    ],
    [
      "-15/4",
      "45/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 9747f1 = LMFDB 9747.d2: https://www.lmfdb.org/EllipticCurve/Q/9747/d/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 9747, minimal discriminant -3518667, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:29:37",
  "updated_at": "2026-09-26 20:29:37"
}