{
  "id": 5603,
  "curve_key": "0:110943665354152845576",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-128407020085825053"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 92.31110845408334,
  "faltings_height": 5.750248280298574,
  "conductor": "2374324244254292909372143153853800689",
  "bad_primes": [
    "3",
    "239",
    "1619",
    "84947",
    "15626293"
  ],
  "discriminant": "-7122972732762878728116429461561402067",
  "regulator": "16275866442094612013.956029825023646465606245175506931727547464",
  "points": [
    [
      "167591442508583633/49021502464",
      "68498144677307587391384423/10853752817549312"
    ],
    [
      "16818426292499202529/18514122262416",
      "-62788236220005759874571517937/79662639327212614464"
    ],
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      "133797018498546523105/218872969454736",
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    ],
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    ],
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      "1616519958166617638247924553/2251025143001842458384",
      "-52531432655501805750755910091686854124955/106799819541586772186069733961152"
    ],
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      "-35998232686840423890987897710712410844796111/256954891822680574688894274665561408"
    ],
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      "38718984383927267264525705201/25853125866924914469604",
      "-7471753008450421349255735151464052995868091/4156900131902221759668098220311192"
    ],
    [
      "9571536975706626418088577349697/158473008833206054385476",
      "29612317387915929656574251988551235477417809605/63085994760113718765901101011585224"
    ],
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      "8319138781841066623182843799556929/6751403194051637086185864900",
      "-732281181603014307677731794569366080555721183887283/554742024693465319001201030890083620643000"
    ],
    [
      "123957364821090108914569979350056545/54496001427702983588975826916",
      "-43403642982339614468140916600319759545734013535483163/12721752919152821185486645129809400427151464"
    ],
    [
      "5826248573341479019049249671620540999381841/9335447416337899143653713007988294564",
      "9659316261682931832377987414374520685401903929186853234081879179/28523492818144252381541675178543159755137135736304409512"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Rank-12 Mordell curve constructed using the Burkhardt quartic family, with parameters (u,v,w)=(-2,-9,-12) and specialization t=407/102.",
  "created_at": "2026-10-23 22:23:16",
  "updated_at": "2026-10-23 22:23:16"
}