{
  "id": 5036,
  "curve_key": "5174144593968:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-107794679041",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 87.82408543669656,
  "faltings_height": 5.386914198032871,
  "conductor": "3449429729312",
  "bad_primes": [
    "2",
    "7",
    "17",
    "31",
    "89"
  ],
  "discriminant": "80162627783461697484809702993018944",
  "regulator": "2330.942761646422577475980810185663238971978036",
  "points": [
    [
      "-281232",
      "89845812"
    ],
    [
      "800513",
      "653218608"
    ],
    [
      "13889953",
      "51752317848"
    ],
    [
      "64841553/64",
      "493955746137/512"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 328321. Found in an ellrank scan of squarefree n <= 6*10^5 with n = 1,2,3 mod 8.",
  "created_at": "2026-10-21 01:49:03",
  "updated_at": "2026-10-21 01:49:03"
}