{
  "id": 5846,
  "curve_key": "0:68154286266567258912",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-78882275771489883"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 91.33661144930275,
  "faltings_height": 5.669040196566859,
  "conductor": "25557857349962722092",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "61",
    "79"
  ],
  "discriminant": "-2688082602144212080617533094824793648",
  "regulator": "112763.91568067279554497888872276313041062449507311",
  "points": [
    [
      "584563",
      "347665108"
    ],
    [
      "640927",
      "429421090"
    ],
    [
      "1559539",
      "1927217956"
    ],
    [
      "2946463",
      "5049877342"
    ],
    [
      "85243291/9",
      "786991699592/27"
    ],
    [
      "142926721/324",
      "486571909663/5832"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-13,-11,24,-1) and specialization t=5/6. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=2918781558. PARI/GP 2.17.4 returned matching computational rank bounds [6,6].",
  "created_at": "2026-10-25 11:06:41",
  "updated_at": "2026-10-25 11:06:41"
}