{
  "id": 5046,
  "curve_key": "4113502639487101488:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-85697971655981281",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 128.582419689552,
  "faltings_height": 8.783442052437492,
  "conductor": "2742335092991400992",
  "bad_primes": [
    "2",
    "17",
    "71",
    "409",
    "593"
  ],
  "discriminant": "40280198566442308430451132553855809873979205914306624",
  "regulator": "467514.134224753821199928201219532463577288881167",
  "points": [
    [
      "-56064813247/1024",
      "69726641521539297/32768"
    ],
    [
      "-16354561527/121",
      "4018177661997672/1331"
    ],
    [
      "3230530672/9",
      "106254576700084/27"
    ],
    [
      "27091467173632/91809",
      "17733982433256526096/27818127"
    ],
    [
      "3641430801144361/7617600",
      "173715534118404406897109/21024576000"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 292742159. 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 01:49:43",
  "updated_at": "2026-10-21 01:49:43"
}