{
  "id": 5821,
  "curve_key": "0:23400282846944229408",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-27083660702481747"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 89.19855956731935,
  "faltings_height": 5.490869206401574,
  "conductor": "108334642809926988",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "59",
    "347"
  ],
  "discriminant": "-316882660484370561431894583050307888",
  "regulator": "186050.225910497241242249541366128871211861536579",
  "points": [
    [
      "300391",
      "4695418"
    ],
    [
      "309127",
      "49561694"
    ],
    [
      "1237873/4",
      "404320553/8"
    ],
    [
      "8672209/4",
      "25504495289/8"
    ],
    [
      "110596411/225",
      "1021894070716/3375"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-18,-1,17,1) and specialization t=23/18. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=63343462. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:01:16",
  "updated_at": "2026-10-25 11:01:16"
}