{
  "id": 5724,
  "curve_key": "0:33006976477962408",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-38202519071716"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 76.07099068491331,
  "faltings_height": 4.396905132867738,
  "conductor": "864848867214699620202458547",
  "bad_primes": [
    "3",
    "5659632455069"
  ],
  "discriminant": "-630474824199516023127592280763",
  "regulator": "23676604646.44744079883208866094719591025392485856822155969",
  "points": [
    [
      "36996",
      "3526195"
    ],
    [
      "66012",
      "15793996"
    ],
    [
      "583158588",
      "14082508226227"
    ],
    [
      "1121514/25",
      "902063588/125"
    ],
    [
      "3449818/9",
      "6405409961/27"
    ],
    [
      "9598956/121",
      "28579175204/1331"
    ],
    [
      "193682409/3844",
      "2257359405377/238328"
    ],
    [
      "255128361/4096",
      "3739140212395/262144"
    ],
    [
      "1755284248/7569",
      "73426869139924/658503"
    ],
    [
      "6965423718/182329",
      "326166541560364/77854483"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed from the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(-18/3,6/3,-8/3) and specialization t=7/179. The specialization was identified using a three-stage Mestre–Nagao sieve involving 328 primes. \r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [10,10].",
  "created_at": "2026-10-24 16:55:47",
  "updated_at": "2026-10-24 16:55:47"
}