{
  "id": 5025,
  "curve_key": "846316848:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-17631601",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 61.669213116828836,
  "faltings_height": 3.2073415047105596,
  "conductor": "564211232",
  "bad_primes": [
    "2",
    "13",
    "17",
    "19"
  ],
  "discriminant": "350796475913120292787264",
  "regulator": "131.95301266788511381750334132107649401032811",
  "points": [
    [
      "-3249",
      "151620"
    ],
    [
      "4225",
      "30420"
    ],
    [
      "25857",
      "4102644"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 4199. Found in an exhaustive ellrank scan of squarefree n <= 20000; one of the smallest n of rank 3.",
  "created_at": "2026-10-21 01:48:13",
  "updated_at": "2026-10-21 01:48:13"
}