{
  "id": 5836,
  "curve_key": "0:2247195505602247200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-2600920724076675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 84.51242934139944,
  "faltings_height": 5.100358354241582,
  "conductor": "3467894298768900",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "37",
    "53"
  ],
  "discriminant": "-2922388680786423279421512552030000",
  "regulator": "19387.6747782836687451957173639050020847682190012",
  "points": [
    [
      "306219",
      "161595972"
    ],
    [
      "313131",
      "167636196"
    ],
    [
      "750841/4",
      "506790739/8"
    ],
    [
      "2771041/4",
      "4594719311/8"
    ],
    [
      "4252521/4",
      "8759900331/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-10,-9,19,-1) and specialization t=6/5. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=19629610. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:04:25",
  "updated_at": "2026-10-25 11:04:25"
}