{
  "id": 5828,
  "curve_key": "0:9051886549260970272",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-10476720543126123"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 87.29900973672416,
  "faltings_height": 5.332573387185309,
  "conductor": "41906882172504492",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "17",
    "37",
    "73"
  ],
  "discriminant": "-47417042882344719902013569524807728",
  "regulator": "46301.4412093841881533087061170666320488513243934",
  "points": [
    [
      "22156303",
      "104290736498"
    ],
    [
      "1720537/4",
      "2103022909/8"
    ],
    [
      "2352571/9",
      "2320126588/27"
    ],
    [
      "5934097/4",
      "14432250599/8"
    ],
    [
      "1430749411/529",
      "54104120829928/12167"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(-10,17,-1,-7) and specialization t=29/16. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=39396786. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:02:37",
  "updated_at": "2026-10-25 11:02:37"
}