{
  "id": 5867,
  "curve_key": "0:44409854071727214424200",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-51400294064499090769"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 104.29549667248168,
  "faltings_height": 6.748947298498435,
  "conductor": "205601176257996363075",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "19",
    "31",
    "43",
    "283"
  ],
  "discriminant": "-1141339779324135559002098045518035033301875",
  "regulator": "42475201.803062335857750534830637224791133896657471",
  "points": [
    [
      "3224788147249/202500",
      "5754006418198778443/91125000"
    ],
    [
      "3578987449/144",
      "-213752919931021/1728"
    ],
    [
      "2147650849/576",
      "9115073604145/13824"
    ],
    [
      "2106273409/36",
      "96653232002269/216"
    ],
    [
      "3150129481/576",
      "-146413729967941/13824"
    ],
    [
      "9809279881/900",
      "952049073068279/27000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, restricted to the plane b=-1 and c=-a-d. For (a,b,c,d)=(-6,-1,0,6), the genus-one square condition w²=D_{a,d}(t) specializes at t=-8/71 and w=245644/5041. After rational cubic scaling, the resulting cubesum curve is u³+v³=2759503285. PARI/GP 2.17.4 ellrank bounds [6,6].",
  "created_at": "2026-10-25 16:46:12",
  "updated_at": "2026-10-25 16:46:12"
}