{
  "id": 5750,
  "curve_key": "0:44778540581741937024",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-51827014562201316"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 90.4965213873649,
  "faltings_height": 5.59903269140537,
  "conductor": "33160980721365768720631700149776",
  "bad_primes": [
    "2",
    "3",
    "2256613",
    "212654879"
  ],
  "discriminant": "-1160369037402030979072344451640961792",
  "regulator": "4997507963083164.70235097126506288169673256220635708199363028",
  "points": [
    [
      "1788607659077506/1624170601",
      "74161416045780386030510/65455699390901"
    ],
    [
      "1796661414305322/1556854849",
      "74860135266432833695458/61428821776993"
    ],
    [
      "7677548129529445/65334889",
      "672719186901534509376539/528101907787"
    ],
    [
      "7723640554384045/1275704089",
      "-678707057718357362295911/45564322946813"
    ],
    [
      "215823221839656085/351218613769",
      "88360616592209587417574291/208145145608218853"
    ],
    [
      "1559562144011296145106/84719120081401",
      "61588868185518182002990192252050/779780112246119142899"
    ],
    [
      "23904837444237737145/61547351324944",
      "39710771544231288115574200659/482852019182666568128"
    ],
    [
      "23924392582267480729/61440953511184",
      "40902981943314510116892600515/481600490348762978752"
    ],
    [
      "502617196592622465/200476480516",
      "-355746543790694169019048767/89762542245116936"
    ],
    [
      "90305489485387088433330/19085443578721",
      "-27137586857289422416206965588924118/83378367422479066769"
    ],
    [
      "186841721391894475897/130500875995204",
      "2531289665637077140649022241357/1490802596104659944392"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rationally 3-isogenous partner of the Mordell curve constructed from the Burkhardt quartic using parameters (u,v,w)=(-9/9,-12/9,-10/9) and specialization t=191/422. \r\n\r\nPARI/GP 2.17.4 independently returned matching computational rank bounds [11,11].",
  "created_at": "2026-10-24 18:43:26",
  "updated_at": "2026-10-24 18:43:26"
}