{
  "id": 6461,
  "curve_key": "740971344997034688:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-15436903020771556",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 123.44021504621936,
  "faltings_height": 8.354924998826437,
  "conductor": "246990448332344896",
  "bad_primes": [
    "2",
    "31",
    "37",
    "41",
    "1321"
  ],
  "discriminant": "235429294601998045159098338237834453206140892647424",
  "regulator": "193741.278569723403280875107613876634234059702687",
  "points": [
    [
      "-30640958",
      "666508569144"
    ],
    [
      "387810062",
      "7234552203816"
    ],
    [
      "-1031437456/25",
      "94096049910072/125"
    ],
    [
      "90386831998/9",
      "27172181716814008/27"
    ],
    [
      "825734771926/1089",
      "740203074134889920/35937"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x, n = 124245334. 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 18:35:08",
  "updated_at": "2026-11-03 18:35:08"
}