{
  "id": 6459,
  "curve_key": "470598688480767168:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-9804139343349316",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 122.0783462528741,
  "faltings_height": 8.241435932714332,
  "conductor": "156866229493589056",
  "bad_primes": [
    "2",
    "7",
    "17",
    "97",
    "4289"
  ],
  "discriminant": "60312648410952447921086153680271701778992178335744",
  "regulator": "177073.110113382910520043693895151531389439756108",
  "points": [
    [
      "-66389904",
      "598560309480"
    ],
    [
      "-245344548862/3481",
      "119911417411211328/205379"
    ],
    [
      "-886120802/9",
      "2812261580128/27"
    ],
    [
      "-725662238/9",
      "13933795025024/27"
    ],
    [
      "3065659198/9",
      "162411001589872/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x, n = 99015854. Found in a local squarefree-parameter search using Monsky 2-Selmer matrices and Mestre-Nagao scoring, followed by PARI/GP ellrank point search. Search performed 2026-11-03. Method reference: Dujella, Janfada, Salami (2009), https://web.math.pmf.unizg.hr/~duje/pdf/Sajad_JIS.pdf.",
  "created_at": "2026-11-03 18:35:00",
  "updated_at": "2026-11-03 18:35:00"
}