curve #3895

y² + xy = x³ − 153412721329927372242905977310395410906519400450x + 23132490049982686051246204487816633958084284661629505715441443983202500

a-invariants

[1, 0, 0, -153412721329927372242905977310395410906519400450, 23132490049982686051246204487816633958084284661629505715441443983202500]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

22071991436840795559592274286251423453065749871509992799646315809967654648461424562760220757187470680301273549014830

discriminant (Δ)

-87501485891086533878062418925933259269222717439652235036424533572447982256630963872956268839925927468284416167227603121189615494641152000000

Faltings height

25.8462

naive height

337.5624

primes of bad reduction

2, 3, 5, 11, 13, 83, 89, 149, 397, 832109, 36236423, 707161227258423212023065904393915739, 552198689667382823495372439957677921201475826204710509

regulator

99053141749780077262915701333922.2595058151012778239385383614734274801560372321417520740486304570

submitted by

Ritik Jain

submitted at

2026-10-04 14:18:24 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-04 14:22:09 UTC

Witness: 29 independent points log in to add more points →

(27619153864830211774428697112130914901287266936100/116840922288982136519643889, -11059363489486633742142096144257082141196504205443022453465442229524474850/1262968342407331191907823057624638496713)
(8223168174100930248442075/36, -608375964373429850664998239962761575/216)
(207049271070690586358756, 15638928404917191901692759340651502)
(225665914338630902418802, 2127998742309258624115933813653346)
(213350888275506104544902, -10638785199855986070730490467288648)
(38493593152905967376463140/169, 5470409294919986554122617722294456550/2197)
(10187808485193081037367900/121, -138401692287119981700348027950248629950/1331)
(386410806837221208855500, 146793848114672940294165194526414950)
(453073539496708362139700, 215940275638428592715511698718019550)
(1759604692810336214153350/9, -667894651360796708662174757794632650/27)
(1075365617507103574494440000/5329, -7701245478062705150598071953196559272350/389017)
(1940432760854321818871469725/8464, -2584606329074868661968084768010522661225/778688)
(86947478830842324653516900/529, -590756221082153978993047977252312185150/12167)
(-296439292386389827365100, 206300930753885345068447633443901550)
(227986973052148518960384230/961, 281648621396987108237582407279154796200/29791)
(138386686317301957528100, -67471757281214225569312935743530450)
(201195840811655922414212, -20269415863538831094892196377199698)
(64535100121199735982696272276005442747896900/426031436863187246169, 510436658916532139635869502070377430810650548540601406219900711050/8793514221947876707759949200803)
(59426603326425122245386415997784984697836230/704363002605554604841, 1941779751611263565680017464992091996191990221635512192774565433800/18693680002771524188195239298389)
(617713173558165768846589100753930619747746782946937732898490002291056936308834745423620/2744741804029731580930768412078818439551283176579520445409183609, 327048251980708275334844761676328664171433923348454123361574067087767093253884210787834048579537900447275635677990514861017720150/143797801216492030281760157124823119322802192703539973329919078220002984069201981039566332102477)
(-1670787117593813309489447008536243192379925013708777271409327793773083597649538794/5373185041389493917884871493603410614501792636554332148201, 79528189808417549095213962807367119151122782090472243333267533728230123646017352314393897619186466553997395969702779641642/393865277246112295768788060397584043733284822319575266980377565197338788019321811437301)
(4272644146936028834478488635318198766805587080953693430065250789824920986790075979944653834179476/20931085753804111676470495879646703523862472220740771136092526037319574921, 1719114651424419766555997672343158369062785627637052869381510700276828354624426087194604583822501841427962253469427314825071725005308548433560678/95760771315381805652304052556228498976647659274390139468918937868319768502296496589679458816923886351388274469)
(58354325867214209822399708589549063181779140656100/601641869690496825968282569, 1412788041439371799702019145810771667443022871496204111067153630144662849850/14757305852245828078042709751207994922747)
(-25497416639740000202188328257079400038343340/60174770912695449409, 51264895525389514078886638616229258616047671139684142045080613970/466790134077844869442012567327)
(35727544580210837383478816896474997604444075074710989934399514516/159887247524159240084169899746666880604025, 194310716202454777584326360572320493025980590140224249460731509139937651636297323112365297104746/63932360434446511509055304928945349426593292029393159068573875)
(3421973392559376953489083532502285020591692383794903121165646758083420681361490/15257155940799056487367381408326497549936073062903018529, 154180870345496243896571272530534701661648414105884821540778846202010394374117432150527690536108070531275335625023820/59595075958969029596063094208776616561003054966619348128638133848531754730275366833)
(-689000656394310937435110927423944697896167737154730945447572988/89539909504898308714580198024726437476681, 4177726970091510377541753438438187480202304620546679707622134987960467759891343075376624635702566/26793224107164962415593219470044374060494378895528307389156421)
(-530530480475158925924697174162286416095696896122831681842110/1608892318231911614994965064267583561, 397109461558021341436113961466088748364779535448507303871317865468091462804221016915663900/2040753110770437653459186175148972027308148398964511941)
(-5081495165478449530131572017272670718732691571313704850/16651085678405630966977170532561, 13846440197413569045416593726431908963865602136250788411371602094506890191437386800/67945990369724098395736170863444164978448409191)

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