{
  "id": 5839,
  "curve_key": "0:2618206226281800",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-3030331280419"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 71.00253166349789,
  "faltings_height": 3.9745335477497865,
  "conductor": "981827334855675",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "23",
    "227"
  ],
  "discriminant": "-3967016113044435245979751875",
  "regulator": "63068.1077428994958696301523354620948252863071857",
  "points": [
    [
      "18781",
      "1895841"
    ],
    [
      "38899",
      "7471880"
    ],
    [
      "56329",
      "13255154"
    ],
    [
      "328909",
      "188623214"
    ],
    [
      "480781/25",
      "252554446/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-4,0,-1,4) and specialization t=-29/6. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=18090765. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:05:06",
  "updated_at": "2026-10-25 11:05:06"
}