{
  "id": 5044,
  "curve_key": "310680471487108800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-6472509822648100",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 120.83262406817464,
  "faltings_height": 8.137625750656044,
  "conductor": "103560157162369600",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "163",
    "641"
  ],
  "discriminant": "17353941477640973293849149577110961666729024000000",
  "regulator": "417973.406936928748807100151412503434112170190235",
  "points": [
    [
      "216558846",
      "2958790267944"
    ],
    [
      "-302706147590/5329",
      "167040440780228400/389017"
    ],
    [
      "-1167556775/36",
      "90566556004925/216"
    ],
    [
      "95759668690/1089",
      "11961091313649800/35937"
    ],
    [
      "276202567504710/3243601",
      "1504112313799692735600/5841725401"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 80451910. 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 01:49:35",
  "updated_at": "2026-10-21 01:49:35"
}