{
  "id": 5050,
  "curve_key": "15323038982371816128:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-319229978799412836",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 132.52766755658607,
  "faltings_height": 9.112212708023662,
  "conductor": "5107679660790605376",
  "bad_primes": [
    "2",
    "3",
    "19",
    "83",
    "211",
    "283"
  ],
  "discriminant": "2082049167740946703750131758091409814554127109358915584",
  "regulator": "133439.462873104010981247304043434475284161382774",
  "points": [
    [
      "-3492723",
      "1055906852481"
    ],
    [
      "6714746262",
      "548278856781264"
    ],
    [
      "-1466398060662/9409",
      "6187805727728388192/912673"
    ],
    [
      "26522265129/16",
      "4060676758380075/64"
    ],
    [
      "354725604844/625",
      "20030236155556172/15625"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 565004406. Found by a Mestre-Nagao sieve over n <= 3*10^9 (n = 5,6,7 mod 8), top candidates checked with ellrank.",
  "created_at": "2026-10-21 01:49:55",
  "updated_at": "2026-10-21 01:49:55"
}