{
  "id": 5820,
  "curve_key": "0:400810876951111200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-463901477952675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 81.06453216482937,
  "faltings_height": 4.813033589527409,
  "conductor": "150304078856666700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "31",
    "73",
    "157"
  ],
  "discriminant": "-92968379098564122335321131230000",
  "regulator": "12487.7738627510202615260943201947874041395071090",
  "points": [
    [
      "1056139",
      "1085165788"
    ],
    [
      "3449761/36",
      "4405826159/216"
    ],
    [
      "6750529/4",
      "17538229633/8"
    ],
    [
      "6750529/64",
      "13638555617/512"
    ],
    [
      "81361639/529",
      "685504850638/12167"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(13,-8,-5,-1) and specialization t=29/1. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=223833330. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:01:03",
  "updated_at": "2026-10-25 11:01:03"
}