{
  "id": 5011,
  "curve_key": "80688:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1681",
    "0"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 33.89503543294952,
  "faltings_height": 0.8928266977206171,
  "conductor": "53792",
  "bad_primes": [
    "2",
    "41"
  ],
  "discriminant": "304006671424",
  "regulator": "20.0624975035754025769379354384241124029425",
  "points": [
    [
      "-9",
      "120"
    ],
    [
      "841",
      "24360"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 41. Found in an exhaustive ellrank scan of squarefree n <= 20000; one of the smallest n of rank 2.",
  "created_at": "2026-10-21 01:47:03",
  "updated_at": "2026-10-21 01:47:03"
}