{
  "id": 5030,
  "curve_key": "2136107568:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-44502241",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 64.44675334898076,
  "faltings_height": 3.438803190723221,
  "conductor": "1424071712",
  "bad_primes": [
    "2",
    "7",
    "953"
  ],
  "discriminant": "5640604089037380350945344",
  "regulator": "669.56984537858352343841568723719390634759801",
  "points": [
    [
      "-5103",
      "306936"
    ],
    [
      "271663",
      "141551592"
    ],
    [
      "-99225/169",
      "353752560/2197"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 6671. Found in an exhaustive ellrank scan of squarefree n <= 20000; one of the smallest n of rank 3.",
  "created_at": "2026-10-21 01:48:28",
  "updated_at": "2026-10-21 01:48:28"
}