{
  "id": 5815,
  "curve_key": "0:911800715614772848200",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-1055324902331913019"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 96.52390625301858,
  "faltings_height": 6.101314763543177,
  "conductor": "1407099869775884025",
  "bad_primes": [
    "3",
    "5",
    "7",
    "43",
    "59",
    "61",
    "73"
  ],
  "discriminant": "-481123000576164276898517697270798751875",
  "regulator": "173998.399982224274754224626480824012654270730044",
  "points": [
    [
      "1211581",
      "850405433"
    ],
    [
      "36847699/25",
      "183140982168/125"
    ],
    [
      "89803651/25",
      "841278591976/125"
    ],
    [
      "3467493211/2809",
      "135280575655683/148877"
    ],
    [
      "13491784299/13225",
      "121881794481157/1520875"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-8,-6,14,-1) and specialization t=31/9. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=395404135. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:59:55",
  "updated_at": "2026-10-25 10:59:55"
}