{
  "id": 5827,
  "curve_key": "0:12466978537193497800",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-14429373306936919"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 87.93923021136943,
  "faltings_height": 5.385925093405747,
  "conductor": "57717493227747675",
  "bad_primes": [
    "3",
    "5",
    "7",
    "31",
    "43",
    "991"
  ],
  "discriminant": "-89945343661367665629716943633451875",
  "regulator": "3828.37070235659603165721069402620592821597887674",
  "points": [
    [
      "306219",
      "119519059"
    ],
    [
      "583699",
      "429464219"
    ],
    [
      "3963009",
      "7888369414"
    ],
    [
      "3963009/16",
      "1771464991/64"
    ],
    [
      "6174921/16",
      "13279490149/64"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-6,-1,0,6) and specialization t=-4/11. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=46235105. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:02:23",
  "updated_at": "2026-10-25 11:02:23"
}