{
  "id": 5840,
  "curve_key": "0:2557872758656800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-2960500878075"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 70.95590470863823,
  "faltings_height": 3.9706479681781475,
  "conductor": "959202284496300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "29",
    "31"
  ],
  "discriminant": "-3786292274003789478784830000",
  "regulator": "207295.657873044590096131099166490866527770610417",
  "points": [
    [
      "14911",
      "595634"
    ],
    [
      "3450889/4",
      "6410552837/8"
    ],
    [
      "65740531/225",
      "532996106804/3375"
    ],
    [
      "71938321/1024",
      "607544875769/32768"
    ],
    [
      "9783390409/595984",
      "556507976885627/460099648"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(23,-14,-9,-1) and specialization t=-14/9. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=17881110. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:05:20",
  "updated_at": "2026-10-25 11:05:20"
}