{
  "id": 6136,
  "curve_key": "124381947840171475462141297197243837538413433857165795386145002561041:-1399986077122160269496026986445097508061210121527293335300408734367367522476422939155134434053653236345",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2591290580003572405461277024942579948716946538690954070544687553355",
    "1620354255928426237842623826904047825796630047766296460750535808450938906083648325701899716245543281"
  ],
  "rank_lower_bound": 31,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 470.40028355410334,
  "faltings_height": 37.06116354926548,
  "conductor": "1075413473803274025243141769186017528342090819446194744875079164135733738827039361102177123780319036017750218919637570450616512175207755732139976965882498",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "23",
    "29",
    "31",
    "37",
    "41",
    "73",
    "83",
    "101",
    "167",
    "5358851",
    "967426487",
    "76418946449",
    "92652111051763",
    "27338097364340897",
    "762711689783399351074329710470861",
    "11387103257065402847125027820559011037097"
  ],
  "discriminant": "-20639005520576921815309816658778439466818230705003700736148272736313465708649442353096764718782649280879006058831915390772142817522874195822267404429462165092704349861318432500149493619817905000480768",
  "regulator": "165857567721817866503350458729662270257.9748485888511688983519966368853811655731046779898296274104730",
  "points": [
    [
      "180207190713143225721996524788121280/169",
      "18335632887633914219122489125826272499636783944410253/2197"
    ],
    [
      "3071891431393529389417468629565602318/3481",
      "937651394385162708595973746837956134372713052277685251/205379"
    ],
    [
      "1414340848737957999873789956562063071074616848822758/225019173273935881",
      "-51595366502911799968541905400180792452642197282755405372897977680128226939069/106740513344867340757962779"
    ],
    [
      "4158265958568359731397649807237995072/841",
      "8077374856526692198999053290986561777996011150264759811/24389"
    ],
    [
      "1549078806286489920197149711556638812/361",
      "-1808410123075376049324567709104115187276889387470444229/6859"
    ],
    [
      "1273366985726600643223662889570229358/361",
      "1308026590736058310246498421373302436996350910539172171/6859"
    ],
    [
      "24704446183899258796682704758964224306/27889",
      "-20839987923687839675561031122448171415874740561697944077/4657463"
    ],
    [
      "19599363233641116532501019620511528884000952519044089567135112229993616172155246/4612317148995163003789496074914815651734287721",
      "-81285680662878562603964547591911442749129356648156296041365969173323438667574296248781361494467450283846257856863801931/313241102211497001410729239586113742950704784511629792020648793193269"
    ],
    [
      "-1627943875452519606228327429900210696/1849",
      "4511163631131384459612056860359914529045678754251294861/79507"
    ],
    [
      "-8457119017683044518594088209448634246/6241",
      "25349471975224165905714189657293606915130750740429187939/493039"
    ],
    [
      "-1860182895788533408874227847243010",
      "1968310289822133537476897783249172618409752192321"
    ],
    [
      "1070818060311093564241560362027286",
      "-8567872772710201939368774566356731840979081438959"
    ],
    [
      "14704527314257584596143217024129496",
      "1772843895313001537293731873020424399113054725205631"
    ],
    [
      "-10798202803025857229545843981586978736/27889",
      "235909551820864419428196076249800392300631422171660141649/4657463"
    ],
    [
      "16576375838750014385527391737684808544/17689",
      "-9104510424879836906690310963245976021886001782062232149/2352637"
    ],
    [
      "101696314710503364835276221111765414",
      "32426773863027176583081945539392168101190708206646641"
    ],
    [
      "944410578823628624174226784149188",
      "3929697895803818003268848667038511516220291707899"
    ],
    [
      "499960240480141689902434904581290",
      "21208068679801724752976945196872619545773081247421"
    ],
    [
      "-134693310696194229524542272323725945976096208742807341681256945505472588102618089266153710098374945657335941755511454/101144743051946613306834813446689921659237785561634604826308091171914584010758203041",
      "1674412680017519373384144894569013131506052519494995320407931648903335543117611423703629446184465823074560556627202724521577342215597781284500302265945634583479767811205678553/32167326943160014733700086822898323039725627091594702422051408485267059439083726880191622857898288322367382614377833808226161"
    ],
    [
      "58418706577833059368648799446136446863391116943480924646171630865936118949590653417343446/69121934317190061921034541443956862497011610876323820025",
      "3350694448322800041446474569394433686098626300147601412321727288966888326034257914709352555640481984494432585408632019153110193391691/574677011317425195198749628198726524455842804506017537862609651876033009619323493875"
    ],
    [
      "2124722574974158235417258950783312083641167480338627527269812108527868391040537601893767228650192510670477733530389529430/1189966027180732419177586181420766332946206522805428438309993779094166923498546824218361",
      "-2127436310680340185038499813518914364310180069080015341921580542131745097664467605812364278611930649663103415379966156549162165835171218474499013418186553034362084681972095171952971/41048930283165608571075400019605542915097063344394365952057558659167688525300190614201416830335424016503072829660105587224861280141"
    ],
    [
      "85534937832882375534409303832603051097600901869300706204568689557636302648401493300622291101502/180115034048637829632763526125544248035054455021694437385430849",
      "53882464003776196673698544975472326646715122673522245311961752207958661326602332130530602211151266279651720813867294211477701069421594816470239/2417268801101625554530219647548539579264587144983737694320538765462183104024934098495893843743"
    ],
    [
      "217249176341559105785779648021036893296280184428341066389789107520608579152515045412622/433071271358647010170741911060753146671904016931660489",
      "6023334274066360053358929299599903682588627998581903151275687064451384585652602218625775296960109867312069340935896607089926771173/284996195388736837388901992000813091134149341387308013668483841064640190840271237"
    ],
    [
      "-20870616638713579346630243591650283205881940224491921031379361676596668609126448881957453562913736703970040454990131613930/32703078797690211343348368695861732617506849032305478414065226741992975003256848333924441",
      "-324687748917676345116625879458181714064695195097250952560281768699530872755174271399880784932633804509576579644535293205589827865729766619353590552992551657155786641281268536440896389/5914022346310936368819446027727438905730992766069687611968572874276988292142187060802293002728243832626756643519419413476722235384739"
    ],
    [
      "-22944516579847261894505738374622244288054144799322430087123571473939970116/38058080997995303318028475468703029057225",
      "404175971836299373744564136713178390049274767576112215282254361717653932652346345038721560787324267407531150943/7424553296132477403390315218207402192733517988065727236917125"
    ],
    [
      "16833170005115398183358551577826381374706732508333424546144406/23792257818463710314659186561",
      "-43601203564817071112632936500167410983120711974337901032789330934059229579946061082137795993/3669893709008729040595536312623128759098559"
    ],
    [
      "1240676094064218974162601386032500374779333778728826288535251615127114520626115677732816923379691381091302378522401661924638025075734016009608830/854279566998203589573117149482537874896512187211633649106262910379398620389370513050766891796048116918101691641",
      "-757429246856112069994505548200438217556134070055110201196023363480632694215935405416087003177677953745493048231039491347211642846467195966874464944966249294034974400056762226944039671213615528101392046801029015193491/24968935546323953700379080868468587532586803617452070423902444423448820036299830266400206812107816945938113239056214951174435015679311548971606325260642307148749522061"
    ],
    [
      "151101383769317217992037305439821273372728373386629484069853763375468823707132616805831525520209858098840164/179503906256456989632839999854071730257724034520045770298106199051348995849",
      "-14337621310962001354813193133037155363029332426463208673918097102574824939471476458194503305368898405186554391504782399421252941427281270347175681727420294679461/2404976603814633711192310537220442608075287161850287437229703878770818522461277242911395113645399772495241401243"
    ],
    [
      "-76197207450997267885625998432410160164491285530670748193736278442583973406500779618803495383023184462329722133876702592032792246/145404882446833741074860459349610858143416764714108682443602753976235701658927235340980164709889",
      "-2951868914832209083392870641917703049610963220724655356341295534383010206528717920220308503532084281434198214092534542020482160784216148813729131552395905385546818013807269692361617495882592349/55445778343959498029074536015419067873530387679689503955849439626932399923596687213650826625144857032901963501305759728705393279932541802220287"
    ],
    [
      "2688676458701727448058409122590373206594620574731986944370106623307333831949675055609/2048004506814267302320565958211455744829797683934784",
      "2032924046057352390910813973138200236116955952366829893969978383826106114238650151941644507402336888047805109331815115008566729/92682205956548741331455641007986743202336543227734462038242564871140205250048"
    ],
    [
      "14874406580733326423203247315793982791611692465044667367786375742366252161357016714343703382813508459186432513190605220761291205051562938046782454894/22195037566683595529589536704636482068164672980529350932628883632402808314565499825516455620492863533930162222677601",
      "1421242790324633409785281528972725502814538353242322138297862249031874112770387513986095833755955133127796553535217331331272463061159218792711176633802537082332349280163864713386561313010234397369652201175680026966805714945/104564394432547661572297112549803290853327464416751255220390686116977432832780287203281528454997966694304386067793827119072880815332324740091443819533605215828201254262104849"
    ]
  ],
  "submitter": "Ritik Jain",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-29 13:55:26"
    }
  ],
  "commentary": null,
  "created_at": "2026-10-29 13:47:21",
  "updated_at": "2026-10-29 13:55:25"
}