{
  "id": 5801,
  "curve_key": "0:169489972271232",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-196168949388"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 65.52762976071459,
  "faltings_height": 3.5182917225178443,
  "conductor": "65389649796",
  "bad_primes": [
    "2",
    "3",
    "17",
    "23",
    "109"
  ],
  "discriminant": "-16624334896124416808203008",
  "regulator": "1483.325421748638211339740304259151783052353908",
  "points": [
    [
      "6213",
      "208953"
    ],
    [
      "10317",
      "949725"
    ],
    [
      "33681/4",
      "5064903/8"
    ],
    [
      "563857/4",
      "423387719/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-18,-1,19,-1) and specialization t=1/6. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=170476. PARI/GP 2.17.4 returned matching computational rank bounds [4,4].",
  "created_at": "2026-10-25 10:55:25",
  "updated_at": "2026-10-25 10:55:25"
}