{
  "id": 2791,
  "curve_key": "223825:-21685625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-4663",
    "23156"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 36.95585932650707,
  "faltings_height": 1.1452971061084596,
  "conductor": "498675",
  "bad_primes": [
    "3",
    "5",
    "61",
    "109"
  ],
  "discriminant": "6216918890625",
  "regulator": "8.7741245546340279741446668963547345931459962",
  "points": [
    [
      "-44",
      "403"
    ],
    [
      "66",
      "58"
    ],
    [
      "80",
      "372"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 498675d2 = LMFDB 498675.d2: https://www.lmfdb.org/EllipticCurve/Q/498675/d/2\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 498675, minimal discriminant 6216918890625, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:22:35",
  "updated_at": "2026-09-26 20:22:35"
}