{
  "id": 3220,
  "curve_key": "49:-12617",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1",
    "14"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "naive_height": 18.885600779855483,
  "faltings_height": -0.36844448337917207,
  "conductor": "4845",
  "bad_primes": [
    "3",
    "5",
    "17",
    "19"
  ],
  "discriminant": "-92055",
  "regulator": "1.85691246761095834313055635623809874641220",
  "points": [
    [
      "1",
      "3"
    ],
    [
      "-2",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 4845c1 = LMFDB 4845.a2: https://www.lmfdb.org/EllipticCurve/Q/4845/a/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 4845, minimal discriminant -92055, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:43:17",
  "updated_at": "2026-09-26 20:43:17"
}