curve #1386

y² = x³ + x² − 114994919248275970093971123295034975587857914586952900x + 14747307816557257001400099596649023123173807379651880915169902184375115920040000

a-invariants: [0, 1, 0, -114994919248275970093971123295034975587857914586952900, 14747307816557257001400099596649023123173807379651880915169902184375115920040000]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 39972448171213477505599887614352279744155388241097685316034780140600321474374081727570335532584009485083202500402660290397425240
discriminant (Δ): 3370405579910297156443952938674629166482117509851729998666150192713415960078337449615016796647182071792114385483389639611343454909518045099455784378582500000000
Faltings height: 29.4019
naive height: 378.1438
primes of bad reduction: 2, 3, 5, 13, 17, 19, 31, 37, 71, 73, 101, 103, 109, 25097, 5828701, 80447085738243464803080503459058290929541626395129246560050844485213299442690495138896770920402717
regulator: 376558509462981228872155972532991.5050913359855790020786637979855561083442783149324292760132582
submitted by: Ritik Jain
submitted at: 2026-09-24 21:23:50 UTC
last updated: 2026-09-24 21:23:50 UTC

Witness: 28 independent points log in to add more points →

(145250591173711100311974155687258667823010/1132737846381241, -55377870357732258031789387207448934610046843507685343188846810/38123618655978778288211)
(4659152653509121468208657790650/6241, -9157279004186433139902539604644763164536791450/493039)
(-90444454054142783121770853097/841, -124049881055273765488421279785527070827968814/24389)
(-7529079905155363538607728367503245634747619551331150175351892183290/23146185708744002636014799525141086046569, -14829845542352910111547289535314749388895068776879429039463898111043812151836665064791822235435882930/3521430730802889872176782113778647165780115223781990413779253)
(601049159524176499039860530, -12757930201175318979337524169220262358530)
(76515953301058074029189351780, -21165266058648821048615735420095201991412720)
(-95316370211712783717175681912514/255025, 302498691098964127759712423945234343190370192034/128787625)
(50730829678291240301788113115, -11426106541361555778033019173799383061733340)
(79703776811524955906748513358380950/8059921, -22488794005002625140693523090356590877996335191904250/22882115719)
(39770605605623400618225369211190/237169, 48904402117898474145505558985421944955323982330/115501303)
(132207160767395166772691960141/484, -20528822008117166885016153519219628180041915/10648)
(-359919300081401867398600101532675/1406596, -8735277748735893161444039982936839286391209211875/1668222856)
(-38950328504894498471459121598870/237169, -624171053382397530612611006590124577164375421690/115501303)
(89208031270236411433455494480/289, -14459960882998802459727524968982922155667840/4913)
(291053384635312481701231460, 2435853615167065173902462203812694171440)
(888509962031691802318267600/9, -56357048428409336632154356425635292437600/27)
(-32112869868165942780092647018848394356411711719/112696547489549712144, -5906994321508315085463632240578608739052413945171713915049178769064955/1196371110074412245684736817728)
(4498847717231009645429000137625600317851344/7527241206105625, 8248161051276367274281910857335155179879891242160581186673716672/653061000688332040671875)
(-585893623205781012211293018288403773107907926312725/2030424142094326816196401, 14145147145503660324289965275153876024068618925245781989188290961957961757700/2893211301843613936553559844994845399)
(-588406327603443755172134998259848280426232433103061733054694665450/4869223042845857029999969804322730544729, 1761550747151969889161183099289812403740880141655946549042274428217699199739557487026317752633771250/339773499222131282158885597988024724660369311988344475051683)
(68765725727328799099577593527405161061605675773291775/395154027037141517954684929, 591496867377203223657473523116790506915762116666923702243810613366999398898050/7855062019003611033645258101509289974783)
(977322717454528725413881175923510266616750/5685095608582329, 104124344852853969368926481927674105201535373277007490968031850/428653781351282741945517)
(-14398081303989161469694962612444019787997325/44800631644590409, 40797521319995661177264084023004683525413263245956348953459760500/9482573240502742379823173)
(76062276622711248607849778673171470/6367880401, 1858430403484239819981431968536435149888664044338624530/508150488119399)
(1567707802188919479245555651006613575/4823441401, 1146136922861076205207505346451103949278607927933057750/334992828740851)
(-215142381683611736674488885442475012908567174310/618849665404136504809, 54881174315080903610321153884142278371580448676627276049072051764454770/15394930785926147228295388848373)
(-81531478682895175345393480480686857628371517638499307570/371666581429212853359588578281, 1228937343074608045461750722143308113391977799381206693080274747660400760031062500870/226584537512734728886467535662883280946941429)
(256577410107320360641572618383012129017116800/1670205750141546409, 1815042532865520059296275364831959866863821007096971408682950765000/2158514457168846790364078827)

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