{
  "id": 5519,
  "curve_key": "223992253336421724688:-3210264499434593637089862308800",
  "ainvs": [
    "0",
    "1",
    "0",
    "-4666505277842119264",
    "3715583909827129765128856436"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 140.5744294254909,
  "faltings_height": 9.645998444103894,
  "conductor": "250961682277448688",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23",
    "29",
    "101",
    "103",
    "199",
    "41609"
  ],
  "discriminant": "539617936470855180403400959802209725801417812733207527424",
  "regulator": "42331.115709793722003713548159716075925823395086077",
  "points": [
    [
      "-2481798550",
      "3272379829056"
    ],
    [
      "926716235",
      "13672028870136"
    ],
    [
      "996765242",
      "7382461065840"
    ],
    [
      "1027062383",
      "2489169822930"
    ],
    [
      "2321332367",
      "73428662844810"
    ],
    [
      "118633242394/81",
      "3471691135406480/729"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (20497,62721) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 6.",
  "created_at": "2026-10-22 21:22:30",
  "updated_at": "2026-10-22 21:22:30"
}