{
  "id": 3134,
  "curve_key": "9649:-243593",
  "ainvs": [
    "1",
    "1",
    "1",
    "-201",
    "198"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 27.52382868606115,
  "faltings_height": 0.3577527717576804,
  "conductor": "22035",
  "bad_primes": [
    "3",
    "5",
    "13",
    "113"
  ],
  "discriminant": "485541225",
  "regulator": "2.79216356466533004739912261607736493849129",
  "points": [
    [
      "14",
      "12"
    ],
    [
      "16",
      "29"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 22035c2 = LMFDB 22035.e2: https://www.lmfdb.org/EllipticCurve/Q/22035/e/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 22035, minimal discriminant 485541225, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:38:51",
  "updated_at": "2026-09-26 20:38:51"
}