{
  "id": 5807,
  "curve_key": "0:262040553778283504928",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-303287677984124427"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 94.03006190217837,
  "faltings_height": 5.89349440097316,
  "conductor": "98265207666856314348",
  "bad_primes": [
    "2",
    "3",
    "11",
    "43",
    "67",
    "79",
    "127"
  ],
  "discriminant": "-39736835546544843547423555793409838128",
  "regulator": "295713.526107895359815021481692870489476144241806",
  "points": [
    [
      "6313627/9",
      "5529589660/27"
    ],
    [
      "67022233/36",
      "535641971165/216"
    ],
    [
      "401651089/64",
      "8044643776441/512"
    ],
    [
      "932356657/256",
      "28379552556631/4096"
    ],
    [
      "3204430629607/32041",
      "5736225893801497826/5735339"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-23,3,-1,20) and specialization t=1/20. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=5723204454. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:58:06",
  "updated_at": "2026-10-25 10:58:06"
}