{
  "id": 5802,
  "curve_key": "0:17833490864928",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-20640614427"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 61.0241986293415,
  "faltings_height": 3.14300579490342,
  "conductor": "27520819236",
  "bad_primes": [
    "2",
    "3",
    "43",
    "643"
  ],
  "discriminant": "-184047104415202792558128",
  "regulator": "369.8051155229239477987213319928894934377045334",
  "points": [
    [
      "13503",
      "1562490"
    ],
    [
      "19651",
      "2750968"
    ],
    [
      "82947",
      "23888736"
    ],
    [
      "857119/289",
      "362588986/4913"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(7,-12,5,-1) and specialization t=1/3. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=55298. PARI/GP 2.17.4 returned matching computational rank bounds [4,4].",
  "created_at": "2026-10-25 10:55:39",
  "updated_at": "2026-10-25 10:55:39"
}