curve #3838

y² + xy = x³ − 5705244439710444308785310874515602905500354081x + 165147595779958764542180306663419525788050523791149214803533520306761

a-invariants

[1, 0, 0, -5705244439710444308785310874515602905500354081, 165147595779958764542180306663419525788050523791149214803533520306761]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

12137785334871009412384689520843085913143094979922413703015371576178629664650093484807131870453212470080532352210

discriminant (Δ)

102846678938888060055163837301227784075290240989448106615489692663015430594501344255394813874342870179116649140708073329563808063825305600

Faltings height

25.1372

naive height

327.6867

primes of bad reduction

2, 3, 5, 11, 13, 19, 23, 103, 14884814129, 60946214353879, 1180866094069801571486774317492117723, 58677647650546669294828767442806476600333263

regulator

10378848727840489870949736787514.68032769865765599263612000955538272474119837641070558326505321

submitted by

Ritik Jain

submitted at

2026-10-03 16:49:50 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-03 16:58:20 UTC

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

(-588191768347501988910950/9, -434412425307531090261708233087528887/27)
(1658140275946887305662026, 2132989522352294713327233113842620267)
(96392609275167478270506, 22601759054269305882333140919670347)
(35088044252591587832746, -2856764543397832325768701362600053)
(12027919423669950215506, -9912893858075958373136643710676653)
(-27631478407302512982819014/361, 84954616887102726100629929970916238713/6859)
(80440350964854338003626, 15057127640247377082936146420061067)
(-63623358468745169304182, -16449662476371590656357302827358005)
(40795186562364250050634, -542550819205389347423053087968917)
(46430079098893930340266, -586849575861092823205808196007733)
(-294925982379804201889072694/3481, -1304580548048010425002993305788878392847/205379)
(261372269156969913771766, -128567968465533540767370763816821833)
(-58883122129241412888234, -17231637769034992295214957977277933)
(86079685949708150484225526/361, 762623003449627411589177880383787930253/6859)
(-20336269466188075474479143276/339889, 3387891307930009460112522933525289957078279/198155287)
(70936574591194441556827279279354/1768959481, -68507118720770804617369528037986745897185929583/74400666811379)
(3962203284854644246406550084038258130866602997550351927352734682/66234178197073722000211571663324685189289, 104978322316228212686498246795093997012999094026191593154046443127341968411291475493346942166599/17046029207070447334962757193666723557702872664314848526706837)
(15634322755967197344571525711865090732387194/482184071566598713225, 39967471786675053963517507333149749632534838459488690491293443817/10588130605919923728265527270875)
(-143054150274417966078006175039485624110966/2308043455129492129, 58742715077780578962466271567521414581904294672617783560715749/3506436447986720095861492367)
(25509970939193380959687583307793794635999551757336/188864047829165602274472961, 111901765387723241545320944760604290867840639666553291363754057598670921003/2595517373253541198087982567180987240959)
(1142315733330342957875382324095100998363462950600199786312975873348921720428509855784065046/16901341003400433313717038484258990242285656609142982012324009109521, 652875503371314668716759643725428971294824343144798810639007651924862381793038202910840398443674952737599495381552404076515623296667967/69483509576872366500973686110659847531567744253433998390199927285558542509805026154708286091201122681)
(-5298276446514496735951132576724958608869503881700439234166/62486178233509075771517006103605809, 97910407946889662195737932138802870069180221724353617768329304694523343055742884730109/15619817124138309793817181204009039784807255649431127)
(-50383761705985882166199162090049711686905023492798364/1296904149043636116625937151481, 26754910827393973172842774279855977185429883094865251960941165903630519018263437/1476936486353747606568691063660709270016196621)
(15722069343887898713380288425835373245915417900173030634/478611751508204331268185473607649, 38014746062942245804205677042915095362577188587301128132236371897289950555064922619/10470683606325389992219655181464633903656901739857)
(-2437247256348344676527841595927463054349146758854766886/33359932964738746476702746988409, 2669892941131625467613337505412568559651640136759995716968327409034303842828387889/192680495245145362987509307641608431589706267827)
(119575933104166694276427377443186945786154931312361090643297396989166944662182309368/3824026510918694548086201734027020285557682095139698028178521, 31122749880474996780292446076716144918263647981791531221135844776594801967982570034885706805859199569824522087537286682979327/7477929074125154854421389188951915466828027905058465738122137172954891217591622769962304931)
(-64402920904305550384023341258987527154528527919904137989258086390847222680714060842865834063592244110393673828886/4743717900297322645177269856221349548543809894977118513900728707326998367119181469244704121, 160094487187291949506414886908317244478645033066014218014430416893240284942876196299973345560805424031698036458247180353638713934460774993587412438816669588366783506878367/10331854504469223052482209768922691266477516358451939293785100342325461048744278895641341462474382824477819583525644450601348412566382669)
(-117275392604189168263655898154597197482539739579847031593654079257393158/1889441766590988381628263658139075885670115039009, 43470048390247097308223123841390083508432903725267471677394138775165794443941097616157105743219980362308779/2597169337963195910141747521587516347918386769711061508920273648571081777)

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