{
  "id": 5800,
  "curve_key": "0:512128008",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-592741"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 40.10817033476017,
  "faltings_height": 1.4000034370216425,
  "conductor": "192048003",
  "bad_primes": [
    "3",
    "7",
    "127"
  ],
  "discriminant": "-151779569778963",
  "regulator": "29.629967505526871749207409459031538546977943",
  "points": [
    [
      "127",
      "1206"
    ],
    [
      "889/4",
      "25777/8"
    ],
    [
      "118237/81",
      "40652272/729"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(20,-20,0,-1) and specialization t=0/1. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=8001. PARI/GP 2.17.4 returned matching computational rank bounds [3,3].",
  "created_at": "2026-10-25 10:55:12",
  "updated_at": "2026-10-25 10:55:12"
}