{
  "id": 5039,
  "curve_key": "13326995531568:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-277645740241",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 90.66243849970326,
  "faltings_height": 5.623443619950095,
  "conductor": "8884663687712",
  "bad_primes": [
    "2",
    "457",
    "1153"
  ],
  "discriminant": "1369786930488155560149026655284321344",
  "regulator": "31521.86776519268782895208347949383848195761704",
  "points": [
    [
      "-346921",
      "233597400"
    ],
    [
      "769129",
      "491365560"
    ],
    [
      "-20330197056/187489",
      "13784651299166280/81182737"
    ],
    [
      "44771833/49",
      "244744295328/343"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 526921. Found in an ellrank scan of squarefree n <= 6*10^5 with n = 1,2,3 mod 8.",
  "created_at": "2026-10-21 01:49:15",
  "updated_at": "2026-10-21 01:49:15"
}