{
  "id": 2676,
  "curve_key": "241:-7145",
  "ainvs": [
    "1",
    "1",
    "1",
    "-5",
    "6"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "naive_height": 17.748336180727936,
  "faltings_height": -0.47738326203943604,
  "conductor": "21443",
  "bad_primes": [
    "41",
    "523"
  ],
  "discriminant": "-21443",
  "regulator": "1.2451011244899535578268621795574659946742513",
  "points": [
    [
      "1",
      "1"
    ],
    [
      "0",
      "2"
    ],
    [
      "-3",
      "3"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 21443a1 = LMFDB 21443.a1: https://www.lmfdb.org/EllipticCurve/Q/21443/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 21443, minimal discriminant -21443, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:17:15",
  "updated_at": "2026-09-26 20:17:15"
}