{
  "id": 6460,
  "curve_key": "623235169389183168:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-12984066028941316",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 122.9211009642787,
  "faltings_height": 8.311665491998049,
  "conductor": "207745056463061056",
  "bad_primes": [
    "2",
    "47",
    "97",
    "12497"
  ],
  "discriminant": "140091607961194413797493447814366293569460290719744",
  "regulator": "734233.808991013845126603374389760433373584049808",
  "points": [
    [
      "-79734654",
      "726882229920"
    ],
    [
      "158127646",
      "1378673127600"
    ],
    [
      "-162462422946558959/6444878400",
      "288669209093450958298056839/517394837952000"
    ],
    [
      "742299817777/256",
      "639047927938010409/4096"
    ],
    [
      "922754418376176/3481",
      "28030391265259381220280/205379"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x, n = 113947646. 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 18:35:05",
  "updated_at": "2026-11-03 18:35:05"
}