{
  "id": 5806,
  "curve_key": "0:146916729792135167911200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-170042511333489777675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 106.68830583030653,
  "faltings_height": 6.948348061650507,
  "conductor": "226723348444653036900",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "37",
    "43",
    "241"
  ],
  "discriminant": "-12491044845379199779072139566727441071230000",
  "regulator": "893076.003489776480518125946584564869926202114368",
  "points": [
    [
      "100432171/9",
      "942899915944/27"
    ],
    [
      "2663871169/36",
      "137460738658753/216"
    ],
    [
      "84502904619/1849",
      "24542584334342172/79507"
    ],
    [
      "537134185281/31684",
      "386732152839950721/5639752"
    ],
    [
      "713440368921/91204",
      "483876339879351069/27543608"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(16,-10,-1,-6) and specialization t=11/4. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=5019111790. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:57:53",
  "updated_at": "2026-10-25 10:57:53"
}