{
  "id": 5816,
  "curve_key": "0:650449011100026450312",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-752834503587993577"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 95.8483891692144,
  "faltings_height": 6.045021673226161,
  "conductor": "1003779338117324769",
  "bad_primes": [
    "3",
    "7",
    "11",
    "13",
    "37",
    "71",
    "127"
  ],
  "discriminant": "-244840229190394868268846859737279516723",
  "regulator": "20595.2038144225541773897094243997544345904727118",
  "points": [
    [
      "5164201/4",
      "9462691129/8"
    ],
    [
      "1707069",
      "2054679763"
    ],
    [
      "10163937/4",
      "31651387925/8"
    ],
    [
      "8979789",
      "26895109468"
    ],
    [
      "70687057/4",
      "594265101405/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(20,-4,-1,-16) and specialization t=25/3. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=333962629. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:00:09",
  "updated_at": "2026-10-25 11:00:09"
}