{
  "id": 5829,
  "curve_key": "0:25094846538678016800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-29044961271618075"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 89.33838836353192,
  "faltings_height": 5.502521606085955,
  "conductor": "38726615028824100",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "31",
    "37",
    "43"
  ],
  "discriminant": "-364439422916550949384740384016830000",
  "regulator": "37616.9980416738209327876586690134560733213161393",
  "points": [
    [
      "746179",
      "621622792"
    ],
    [
      "5495959/9",
      "12034731898/27"
    ],
    [
      "45917851/121",
      "212980112324/1331"
    ],
    [
      "396950071/9",
      "7908675427394/27"
    ],
    [
      "109592790951/196249",
      "33117115324935474/86938307"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-6,-1,11,-5) and specialization t=-29/10. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=65596930. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:02:52",
  "updated_at": "2026-10-25 11:02:52"
}