{
  "id": 5842,
  "curve_key": "0:1814204714119200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-2099773974675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 70.26884718512439,
  "faltings_height": 3.9133931745519943,
  "conductor": "680326767794700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "61",
    "211"
  ],
  "discriminant": "-1904709921720097337865630000",
  "regulator": "6941.57329410160688689807818460799819445733095574",
  "points": [
    [
      "12871",
      "180194"
    ],
    [
      "100711",
      "31927766"
    ],
    [
      "6190951",
      "15404090026"
    ],
    [
      "2561329/196",
      "996511433/2744"
    ],
    [
      "7194889/484",
      "11592304763/10648"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-14,-1,1,13) and specialization t=-1/14. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=15059070. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:05:47",
  "updated_at": "2026-10-25 11:05:47"
}