{
  "id": 5837,
  "curve_key": "0:8528801667328800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-9871298226075"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 73.36445052411749,
  "faltings_height": 4.171360119468086,
  "conductor": "3198300625248300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "43",
    "59"
  ],
  "discriminant": "-42095172384624142861879230000",
  "regulator": "34856.2883180727808876607744757538755308876866187",
  "points": [
    [
      "27391",
      "3267914"
    ],
    [
      "111241/4",
      "27290939/8"
    ],
    [
      "899431/25",
      "757218046/125"
    ],
    [
      "3062761/64",
      "5112977909/512"
    ],
    [
      "12118561/100",
      "42069641809/1000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-6,23,-1,-17) and specialization t=30/7. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=32651190. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:04:39",
  "updated_at": "2026-10-25 11:04:39"
}