{
  "id": 5804,
  "curve_key": "0:4551735851208",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-5268212791"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 58.29305956379318,
  "faltings_height": 2.9154108727743933,
  "conductor": "21072851163",
  "bad_primes": [
    "3",
    "7",
    "13",
    "307"
  ],
  "discriminant": "-11989756515724662219363",
  "regulator": "75.37817404100820867916165620718631670152245298",
  "points": [
    [
      "3081",
      "154849"
    ],
    [
      "3991",
      "241455"
    ],
    [
      "6447",
      "512536"
    ],
    [
      "83811/25",
      "22503191/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-17,-1,1,16) and specialization t=-1/17. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=27937. PARI/GP 2.17.4 returned matching computational rank bounds [4,4].",
  "created_at": "2026-10-25 10:57:26",
  "updated_at": "2026-10-25 10:57:26"
}