{
  "id": 3146,
  "curve_key": "158025:42514875",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-3292",
    "-48384"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 35.9115255820215,
  "faltings_height": 1.0245365056120792,
  "conductor": "4450",
  "bad_primes": [
    "2",
    "5",
    "89"
  ],
  "discriminant": "1237656250000",
  "regulator": "4.95646172863099317361862972489699377417346",
  "points": [
    [
      "109",
      "883"
    ],
    [
      "153",
      "1659"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 4450c2 = LMFDB 4450.d2: https://www.lmfdb.org/EllipticCurve/Q/4450/d/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 4450, minimal discriminant 1237656250000, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:39:29",
  "updated_at": "2026-09-26 20:39:29"
}