{
  "id": 5819,
  "curve_key": "0:680464107516679200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-787574198514675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 82.12310294266005,
  "faltings_height": 4.901247821013301,
  "conductor": "255174040318754700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "31",
    "43"
  ],
  "discriminant": "-267957987047726128549714233630000",
  "regulator": "45225.8394539718495042643015059165156802777063102",
  "points": [
    [
      "94471",
      "7453706"
    ],
    [
      "201799",
      "86198918"
    ],
    [
      "235339",
      "110664112"
    ],
    [
      "2080039",
      "2999771762"
    ],
    [
      "24746371/25",
      "123052623044/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-6,-1,10,-4) and specialization t=-2/23. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=291647070. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:00:49",
  "updated_at": "2026-10-25 11:00:49"
}