{
  "id": 3856,
  "curve_key": "19014615637901397203013328265438695637901476684177491310358976:-82689310331588340260869327362922629085621192475641872965240629159460352555289298172273956224",
  "ainvs": [
    "0",
    "1",
    "0",
    "-396137825789612441729444338863306159122947430920364402299145",
    "95705220291190208635265425188435811796057620477342353004222218733371462610166936602328475"
  ],
  "rank_lower_bound": 31,
  "torsion": [],
  "naive_height": 423.30094052157796,
  "faltings_height": 33.08639157898474,
  "conductor": "82582328249147274857026635857653639568961319560206085842363663914025091496016797175101213406804181966220325029887959607170978084987697882475700638440",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "31",
    "43",
    "107092614148909",
    "471295584708747901",
    "18784691369628015935789611",
    "659080850733822298324282093",
    "43440258427674094391911151272379846808024091633115954483"
  ],
  "discriminant": "21596569454455944297208519105357470002904321244182250249803781015238618609142093827615362368303743697208709806598798524717483073207400511417365971793745982869786314889950900000000",
  "regulator": "223318337218975847641825676467756421334.4243798435846272315251189682069730704111060977319855266088482",
  "points": [
    [
      "14626731499021214914143566045485/484",
      "-3081696198053973329219530642624820529207937105965/10648"
    ],
    [
      "16956150110090577658384192950595062530245994618145139287123979805713383751615/186020261107309837433844609590404368770660908609",
      "19710267877136133231376529268626896929765878389096031556820675439817252312464450003758787570496326655227849901843750/80230661775157686789385361976182081733035700864869193150875228939666273"
    ],
    [
      "-603131103168054223322148272278490/841",
      "2552284740137189779247049151409302559119390183875/24389"
    ],
    [
      "2633969921395467050760571536735",
      "4162480049379104242187433366081160536219843750"
    ],
    [
      "-653696109716762637861154489265",
      "274449388721128485485988957376954755357519750"
    ],
    [
      "3007084051847809593375349695565/4",
      "-3775889258955709469756950298913248502491302125/8"
    ],
    [
      "-615845990296917712172959655690",
      "325723029270732207644292507061531898637385575"
    ],
    [
      "-51100007875471405980354918725865/121",
      "576617137635308512705144018426191169603990950450/1331"
    ],
    [
      "874574293902800535026823824935",
      "-646682161468296983776609184101654037392497450"
    ],
    [
      "-725037018240147472801890687515",
      "-42229222060453079327453158651405095267966750"
    ],
    [
      "72831936274273215490589374260054310/121",
      "-19655429885169562198569889079214353256376523614696875/1331"
    ],
    [
      "304894807543927274033674683775",
      "57167584129848972463903392137652640055793690"
    ],
    [
      "139262063551262184519613094511295/529",
      "-1196103951400126623396874209999288705259373672790/12167"
    ],
    [
      "3036900103927763665571525953900465/7744",
      "17586697148912431124219931417371178874079207663625/681472"
    ],
    [
      "606418923438661155231073453285",
      "280154623151342015065578412840805760907476450"
    ],
    [
      "3473569602603766833553500661015/9",
      "472342934908713442813281954359002416165399550/27"
    ],
    [
      "32152727584775109694038416306523510310/376010881",
      "-1822174978663060006365670806813913566660267377527607874975/7291226993471"
    ],
    [
      "9824837752966994909390564911815812942338257818012611656687116641032416560049124521835426392740505419137165850791535/14309673271245143363797216814305841822910304748796273845988442121109664052864222720809",
      "20780916549532911973279356433025679254079561860246549225554929241924071065935062584051636429854248006322645719398248335248534024090507323429320105671412562243486440470771310/54130816332864245077200450051621925699366079255857893475652447195564524049810657871961824960452135369455073349576585888721729877"
    ],
    [
      "-188435692565664233351438007265616758552790739348463493541312650/537449276362862351892993769589161",
      "5452373361841407648538211696736264604156892033712720346620547503923930364085384825260933592635/12459660926216049040835901923267104677348261447659"
    ],
    [
      "-9498099787759012745592626859661184623024880706914715685910634733893388055113224265382338554647057525146107491140039236215412515/19236065421552929026352963844237163262052483887548207536593585602550904580469945134966136848174801",
      "34879782132394561050194871346918342186265334414183493780880474686996339185332371350289114300249617165664911688096017568754122910912614326425910568292226411989586477163859138116979180256639750/84367342254437693741605768049079779035911502358567298731847736562682968193793592437823364388023181597247332216666477344543276541785645352318402201"
    ],
    [
      "54452549536914132368232640061794926462657680198028614785904609960410704685/96787112568358562879681457970307875893831076",
      "214850969781797213047725966611267273153550913436580682301557031666785120303758051232555077425229400620634973325/952195885964023533133917972413099298596836568387531423524277963176"
    ],
    [
      "10588376307545290129197487436080731360768726539693433043651282720970052807409597903220325869797/38351013996139636788647095930352637786366783684898746298775048929",
      "645219745483727402603788250969938495385121191499944404104680536610309057411432567883946631390797984434209495943232473146621258804222178081438/7510438197209702262651550724753467557432876907797533239202824779199450469577317541685734093201967"
    ],
    [
      "8854700733516079801951931591095129315782342191793739774198030418984719820062098783933228115/33678938052888686267045218561194649904377692489034184246576361",
      "19277879226566668607173640301084762374846927183640236188055893709358963253637888522782786277906995413301048019351704993448600258644330670/195450859069588251335000135835804263109672620841664540407417954691487326094401610745292170891"
    ],
    [
      "19562748099706879371588074956229060573612147981552378331953308267713359337359395260906139887896335312172405065261362692702067544982490109002483145784135597614591983325567065133870394518813899315119335/114204929223358160071361783534504906719366492453430817411777071319830076442155096056602373525538955241539624685972045147476696522052041789428917307286320516699203492141161",
      "221288782064116994973882213188682457336053751650512799591016336626126896126636781225204280584330386800484751619491646477448646628941963443131976188817776560045054161692480048733330685756980889588585540536057801881009618071293023257305518597873153181163772903259069198053550594118583642834689003581250/1220470463302535369156877217935529900989479194512464910454844419396585912260913203025743712868877892421657706405211877724769028358715182195935521652304336662454519525878097676233471238195539712762886670851772526210100589925668547410334416964679817790614091"
    ],
    [
      "-362477496745979210832959699927735075788864828151727825714145016106052602426699097795534922055976310244154360541640593215816685/788210868168651978829869977165243171064508943704468563147500659858223878279090691273620777755129",
      "297406067898154593348394787630282509553127162567194457514848582567346544617695655845073376128752695075126227545661302318002257296248192024356602706038450726993382142270786757836655136262750/699783387269154679057328755686236920271828864437310482251767039522090592756661336980312694090455748803848193191328832458683865876116346055109133"
    ],
    [
      "43481443828161447925783643658199232568538307804777930576422228523275144956957365545525044561059596360284743084974318451144465703845008130581786580106105960214109078916317434227265/145949993468901684106057235641478577609571349799320532801529330577922310800174442248152103721780444035807853609130663707552296960619319276433213818944",
      "3583328685443466221596374355572275409621470915013604538846252578329624483057423845856747407266279828019606246924726655387988433030243427528759485605953772868790149677897943753183425519990657827687325105367352769194977441279321393277589754875485733017191487642082638975/55757862920940188189792327431052183364632828722789079427153737770129043875188778718945554902102360726315866168708259700864417821288715169967328518178762042802502390694226515945688896285173388378313641373225216286177229839872"
    ],
    [
      "18464259631798898590470306802220586848630301122110522007854340165180841920616117908043459476570104244458699420265779803166516158581519981950747187046489361820986156435/58423708928006552557046842033760193264645474659526300679748378986205750351788701722126159065885335903810951406219110420629792616526496569",
      "643463115684918072069002627235856436214384013080476450206038407463954447601585662320824631409159292514414953304156297293785290941673055410266941909843706898582413546765373188221347553191297274717573559859110966708440691519863649059630504095795834910/14121592851377552854249951952445038155178635659106107150585672623780600112620134511148344180840869140376793724973624681462752247102953708067089580553577460225446866872900725075609290529936518757945248901997"
    ],
    [
      "104528875176855221237965719629830062480194402971696718193519204503705605087270873285/601541595638474006825567014732302285272229699710137561",
      "83610222317870342002205059336879750835390840421311763665935656006124679689847129162920514002010265114840729839101637282483550/466550323849403146678377860553410554918308113215006027520414039410441612286822941"
    ],
    [
      "-33406503155764835978156193061598606113416233652449384699701067460634174129943236943266957596949387739071113134498387792385728286947927619900004038370025/207886390973135188938273419378347684073103576336529613132818089398792886909321663862489530590931013889107600869882471535921",
      "1180873933551275328107403856153017715196764564982713582110955428635033156747587384899025688161296554412513500660427225109231863819678715557959867022079559911329375764029748340832397574213930536670163077182345157553323018926868090/2997361257788867903382184049607213328413793367113480463624920233786620312915703314759173611145420400699695446478599647591117476086529476465989650589686000582775635227891465238411338281"
    ],
    [
      "184155761859448329749694452394774975770204078797228602566933875767315024193439763358205085470497638670043288046951173140603798735079294228752576636877039577576568045/18221515102188672858762188288198573104741589951220705019989283983118617054069136487488106573137946930674375077115747575627355331716516",
      "2494332647285828527223365258213481558745954446348412346366522326946592036955922162661604774135728572916426468843968342447875975739506807522528079390718870434153481707214935544910481894526020270427799451524874593956469638203311769189943066591391315/77781574113832590840166496089134699914313069409431922713359636540915639626608712288288065901110341754866397826618058075004383854324973423576590022719192306190723314525625047869089753271054473448049064"
    ],
    [
      "1774956442998754269821016324899929633947177398399952271859514954222862682740748459730742070638140674442182808991176733285/4605903354940681246595048849186719868847224126048671784344942388406761131364435643439475881",
      "164422188844368493719292292787482606495388187352201067365125465737801941443683063230098167477278983171645012640470029895319960056418336471334002291792433097859703097083690324077250/9884898891836874496074271726921524079370948505287349624611790325280891040224454676172954615132175762632105097492278883673934668616252779"
    ]
  ],
  "submitter": "Ritik Jain",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-04 00:45:01"
    }
  ],
  "commentary": "Specialization at T = 50572/75477 of the rank-17 fibration of X1152 given by:\r\ny^2 - (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pq(L+p+q) - pE - qD,\r\nL = 592163T^2 - 29368T + 105142,\r\np = 156249T^2 + 37094T - 70848,\r\nq = 134718T^2 - 152405T - 32203,\r\nD = 25614574794T^4 - 32707026159T^3 + 2215089367T^2 + 427950124T - 617483196,\r\nE = 3(1895006208T^4 + 8874840900T^3 - 5897289076T^2 - 684372525T - 81082157).",
  "created_at": "2026-10-04 00:07:50",
  "updated_at": "2026-10-04 00:45:01"
}