{
  "id": 3231,
  "curve_key": "2208:-103680",
  "ainvs": [
    "0",
    "0",
    "0",
    "-46",
    "120"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "naive_height": 23.099527222190957,
  "faltings_height": -0.3145323002463064,
  "conductor": "4352",
  "bad_primes": [
    "2",
    "17"
  ],
  "discriminant": "8704",
  "regulator": "1.88143684322227386875464464983028979652256",
  "points": [
    [
      "2",
      "6"
    ],
    [
      "12",
      "36"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 4352h1 = LMFDB 4352.a2: https://www.lmfdb.org/EllipticCurve/Q/4352/a/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 4352, minimal discriminant 8704, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:43:46",
  "updated_at": "2026-09-26 20:43:46"
}