{
  "id": 5822,
  "curve_key": "0:23282703710636682312",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-26947573739162827"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 89.18848485757105,
  "faltings_height": 5.490029647255883,
  "conductor": "107790294956651307",
  "bad_primes": [
    "3",
    "7",
    "11",
    "13",
    "17",
    "47",
    "79"
  ],
  "discriminant": "-313706187544730981108676457989822723",
  "regulator": "17913.1135501476135875306333655021996690778236580",
  "points": [
    [
      "309127",
      "50916092"
    ],
    [
      "319683",
      "75651439"
    ],
    [
      "342939",
      "115691431"
    ],
    [
      "486759",
      "297291676"
    ],
    [
      "3214029",
      "5759680153"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(24,-18,-1,-6) and specialization t=25/6. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=63184121. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:01:30",
  "updated_at": "2026-10-25 11:01:30"
}