{
  "id": 5809,
  "curve_key": "0:6995920087251909223200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-8097129730615635675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 100.59922817466398,
  "faltings_height": 6.440924923680293,
  "conductor": "32388518922462542700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "67",
    "241"
  ],
  "discriminant": "-28323436265749283077797656882831728830000",
  "regulator": "115644.674687303589424606715110551788100162826912",
  "points": [
    [
      "2147551",
      "1344366926"
    ],
    [
      "62839081/16",
      "463648556629/64"
    ],
    [
      "1200481009/16",
      "41593817161673/64"
    ],
    [
      "1458187129/256",
      "54449151939917/4096"
    ],
    [
      "4383151591/729",
      "284731790870114/19683"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-11,-5,-1,16) and specialization t=1/16. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=1095251010. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:58:33",
  "updated_at": "2026-10-25 10:58:33"
}