{
  "id": 3301,
  "curve_key": "13786321:-51188520761",
  "ainvs": [
    "1",
    "1",
    "1",
    "-287215",
    "59126300"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 49.317562279944504,
  "faltings_height": 1.4444507346258824,
  "conductor": "226005",
  "bad_primes": [
    "3",
    "5",
    "13",
    "19",
    "61"
  ],
  "discriminant": "13786305",
  "regulator": "56.5445426178914001589187972277944433346176",
  "points": [
    [
      "3070/9",
      "22250/27"
    ],
    [
      "112485/49",
      "36394987/343"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 226005g1 = LMFDB 226005.b4: https://www.lmfdb.org/EllipticCurve/Q/226005/b/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 226005, minimal discriminant 13786305, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:54:11",
  "updated_at": "2026-09-26 20:54:11"
}