{
  "id": 5748,
  "curve_key": "0:34849422668025628723232928",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-40334979939844477688927"
  ],
  "rank_lower_bound": 13,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 117.6261576054583,
  "faltings_height": 7.859835709579821,
  "conductor": "24393495144904469512782813122768868609422244",
  "bad_primes": [
    "2",
    "3",
    "7",
    "140983",
    "1714441",
    "486517463"
  ],
  "discriminant": "-702825382114987575602298411693216642374673694128",
  "regulator": "23954588389211488506.62523971304230226376068152351228482036150580",
  "points": [
    [
      "66695433352569486763459/1943089157835225",
      "877355552541916550486654835553198/85652312475618268084125"
    ],
    [
      "1097546904603339870323/13277722441",
      "36360900802757256184737536726790/1529978679153989"
    ],
    [
      "4373883812783919231329491/6113958369158025",
      "-9146963370213831025546721781468795586/478061440579322304985125"
    ],
    [
      "102624099730370899450063/1409720063045121",
      "-31109585327612759057096870549598500/52929686410187180849919"
    ],
    [
      "6322580762612978920342483/141261620631841161",
      "-11791816144677499410753536619666314110/53092879085963933908335909"
    ],
    [
      "1883971833813392432627/48430506395209",
      "-45880782427488891142312454701530/337037725397057658427"
    ],
    [
      "3489079533839000037839/101655898827025",
      "10142077483484314200872561363688/1024941025408032346375"
    ],
    [
      "330115469076200041644067/9530419408033689",
      "32546390935194166068985969707902630/930396396744099586455363"
    ],
    [
      "264927420439655256293150441/2924222437281640000",
      "4193536955629077294856732521951105328011/5000525054914859082712000000"
    ],
    [
      "1382513299250611817720574619/2157766817258549025",
      "51400894194353032012505462315654704772278/3169616836955021813927192625"
    ],
    [
      "61471381701815036935193/967095928563556",
      "13992884055487521566238152367709155/30074909724393606038296"
    ],
    [
      "68082770321656705670321/379990694222500",
      "17702217082492036454336542259455881/7407291599222170375000"
    ],
    [
      "6331920499666364884597775963/98247230777134240321",
      "-464344767861225281168869637184596314501890/973824007940397000833404329631"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rationally 3-isogenous partner of the Burkhardt-quartic Mordell curve constructed using parameters (u,v,w)=(13/9,4/9,16/9) and specialization t=119/4. \r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [13,13].",
  "created_at": "2026-10-24 18:41:53",
  "updated_at": "2026-10-24 18:41:53"
}