{
  "id": 5814,
  "curve_key": "0:3973852865678176800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-4599366742683075"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 85.65253558619806,
  "faltings_height": 5.1953672079748,
  "conductor": "1490194824629316300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "89",
    "421"
  ],
  "discriminant": "-9138603355358019597669553108830000",
  "regulator": "173731.117455448734639200737065552263677226761062",
  "points": [
    [
      "417211",
      "260811184"
    ],
    [
      "2875009/4",
      "4844536673/8"
    ],
    [
      "3733849/16",
      "5763412957/64"
    ],
    [
      "11513929/64",
      "17908423483/512"
    ],
    [
      "12868441/36",
      "43776526339/216"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-20,-3,-1,23) and specialization t=-13/7. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=704791890. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:59:42",
  "updated_at": "2026-10-25 10:59:42"
}