{
  "id": 5833,
  "curve_key": "0:3979657168745731200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-4606084686048300"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 85.65545470194587,
  "faltings_height": 5.195610467620451,
  "conductor": "4606084686048300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "463"
  ],
  "discriminant": "-9165318970341023874721411008480000",
  "regulator": "396072.454155119951507171017505405621457504379434",
  "points": [
    [
      "15171121/36",
      "57244457431/216"
    ],
    [
      "9811093621/1521",
      "971789949540431/59319"
    ],
    [
      "21165807481/47524",
      "2997950715166771/10360232"
    ],
    [
      "22689441229/43681",
      "3361082503752883/9129329"
    ],
    [
      "220996352941/958441",
      "82085194642698611/938313739"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-21,-1,6,15) and specialization t=-12/7. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=26122460. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:03:45",
  "updated_at": "2026-10-25 11:03:45"
}