{
  "id": 5798,
  "curve_key": "0:1768459392",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-2046828"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 42.58674920902824,
  "faltings_height": 1.6065516765439822,
  "conductor": "165793068",
  "bad_primes": [
    "2",
    "3",
    "7",
    "59"
  ],
  "discriminant": "-1809866100204288",
  "regulator": "138.06675967163682156893120853026323398116052",
  "points": [
    [
      "133",
      "553"
    ],
    [
      "973",
      "30317"
    ],
    [
      "3409/16",
      "176729/64"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(2,-17,-1,15) and specialization t=-1/13. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=14868. PARI/GP 2.17.4 returned matching computational rank bounds [3,3].",
  "created_at": "2026-10-25 10:54:45",
  "updated_at": "2026-10-25 10:54:45"
}