{
  "id": 5844,
  "curve_key": "0:1923691732099200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-2226495060300"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 70.38604502383112,
  "faltings_height": 3.9231596611108883,
  "conductor": "180346099884300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "31",
    "397"
  ],
  "discriminant": "-2141545069529409874790880000",
  "regulator": "6145.51980191549635433833323870312202217913021595",
  "points": [
    [
      "28861",
      "4670491"
    ],
    [
      "86149",
      "25241657"
    ],
    [
      "52801/4",
      "2170399/8"
    ],
    [
      "529201/36",
      "210535849/216"
    ],
    [
      "1053241/64",
      "764666861/512"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-5,-1,1,4) and specialization t=-5/4. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=15506820. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:06:15",
  "updated_at": "2026-10-25 11:06:15"
}