{
  "id": 5018,
  "curve_key": "1244208:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-25921",
    "0"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 42.10202922263045,
  "faltings_height": 1.5767428468606945,
  "conductor": "829472",
  "bad_primes": [
    "2",
    "7",
    "23"
  ],
  "discriminant": "1114641555517504",
  "regulator": "15.0626285004700100769351514769163228071357",
  "points": [
    [
      "-63",
      "1176"
    ],
    [
      "289",
      "4080"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 161. Found in an exhaustive ellrank scan of squarefree n <= 20000; one of the smallest n of rank 2.",
  "created_at": "2026-10-21 01:47:29",
  "updated_at": "2026-10-21 01:47:29"
}