{
  "id": 5000,
  "curve_key": "1728:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-36",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 22.364159848092005,
  "faltings_height": -0.06807960101750936,
  "conductor": "576",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "2985984",
  "regulator": "0.8886258748396192397941873349806892865718",
  "points": [
    [
      "-3",
      "9"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 6. Found in an exhaustive ellrank scan of squarefree n <= 20000; one of the smallest n of rank 1.",
  "created_at": "2026-10-21 01:46:10",
  "updated_at": "2026-10-21 01:46:10"
}