{
  "id": 5813,
  "curve_key": "0:1985196985835196395808",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-2297681696568514347"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 98.080010198574,
  "faltings_height": 6.2309900923394625,
  "conductor": "3063575595424685796",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "89",
    "181",
    "199"
  ],
  "discriminant": "-2280675389218257499640838829473769328688",
  "regulator": "34884.0588496190135691480911594587490577730444833",
  "points": [
    [
      "9833187",
      "30797541684"
    ],
    [
      "5294793/4",
      "1177713243/8"
    ],
    [
      "9547993/4",
      "26895784643/8"
    ],
    [
      "257427793/64",
      "4056744582233/512"
    ],
    [
      "9795258993/1936",
      "960809024860425/85184"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(17,-18,-1,1) and specialization t=11/6. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=583435762. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:59:27",
  "updated_at": "2026-10-25 10:59:27"
}