{
  "id": 5799,
  "curve_key": "0:536608800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-621075"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 40.201559790748135,
  "faltings_height": 1.4077858916873063,
  "conductor": "201228300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13"
  ],
  "discriminant": "-166637155230000",
  "regulator": "41.913963818865039378260571348651601785800765",
  "points": [
    [
      "91",
      "364"
    ],
    [
      "1729/4",
      "71617/8"
    ],
    [
      "1729/16",
      "51233/64"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-22,-1,3,19) and specialization t=-17/12. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=8190. PARI/GP 2.17.4 returned matching computational rank bounds [3,3].",
  "created_at": "2026-10-25 10:54:58",
  "updated_at": "2026-10-25 10:54:58"
}