{
  "id": 5818,
  "curve_key": "0:687166178573118183552",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-795331225200368268"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 95.95821565414555,
  "faltings_height": 6.054173880303758,
  "conductor": "265110408400122756",
  "bad_primes": [
    "2",
    "3",
    "31",
    "71",
    "127",
    "307"
  ],
  "discriminant": "-273262359360406567011530706498810163968",
  "regulator": "38459.0697776859204189147423142260644981324610652",
  "points": [
    [
      "1846453",
      "2345196097"
    ],
    [
      "2222373",
      "3190742793"
    ],
    [
      "8460613/9",
      "5082411095/27"
    ],
    [
      "556645953/16",
      "13133016277857/64"
    ],
    [
      "309415495341/126025",
      "167424299771191389/44738875"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-17,-1,20,-3) and specialization t=3/4. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=343259156. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:00:36",
  "updated_at": "2026-10-25 11:00:36"
}