{
  "id": 5831,
  "curve_key": "0:59507577641787912",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-68874511159477"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 77.24976010935487,
  "faltings_height": 4.495135918237868,
  "conductor": "22315341615670467",
  "bad_primes": [
    "3",
    "7",
    "13",
    "31",
    "43",
    "79"
  ],
  "discriminant": "-2049277660181375343698016197523",
  "regulator": "1755.65697467045137442309409905097152493433201033",
  "points": [
    [
      "121303",
      "41424974"
    ],
    [
      "166453",
      "67401575"
    ],
    [
      "737149",
      "632842416"
    ],
    [
      "4234321/64",
      "7606845991/512"
    ],
    [
      "1368991/25",
      "1220455414/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-9,-1,7,2) and specialization t=13/2. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=86246433. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:03:19",
  "updated_at": "2026-10-25 11:03:19"
}