{
  "id": 3295,
  "curve_key": "54193:-12592009",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1129",
    "14480"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 32.70092108338643,
  "faltings_height": 0.5222151793346785,
  "conductor": "12207",
  "bad_primes": [
    "3",
    "13",
    "313"
  ],
  "discriminant": "347057217",
  "regulator": "2.40548049928273706958080543195754910568476",
  "points": [
    [
      "17",
      "8"
    ],
    [
      "23",
      "17"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 12207e1 = LMFDB 12207.b3: https://www.lmfdb.org/EllipticCurve/Q/12207/b/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 12207, minimal discriminant 347057217, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:53:13",
  "updated_at": "2026-09-26 20:53:13"
}