{
  "id": 5824,
  "curve_key": "0:218427374579806728",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-252809461319221"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 79.85045994481897,
  "faltings_height": 4.711860904526542,
  "conductor": "81910265467427523",
  "bad_primes": [
    "3",
    "7",
    "19",
    "31",
    "61",
    "73"
  ],
  "discriminant": "-27610253452446295361875223283603",
  "regulator": "2246.14854167732547611736400018040405779973602941",
  "points": [
    [
      "83731",
      "18281645"
    ],
    [
      "592249/4",
      "437672007/8"
    ],
    [
      "251503",
      "125122742"
    ],
    [
      "592249/9",
      "153096353/27"
    ],
    [
      "2622817/36",
      "2499544493/216"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-8,-1,2,6) and specialization t=-22/17. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=165237471. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:01:43",
  "updated_at": "2026-10-25 11:01:43"
}