curve #6145

← home · all curves · JSON ↓

y² + xy = x³ − 3142421283069034024441164447496460419735x + 38741772174151726531043311070093060947931828774707414037225

a-invariants

[1, 0, 0, -3142421283069034024441164447496460419735, 38741772174151726531043311070093060947931828774707414037225]

c-invariants

[150836221587313633173175893479830100147281, -33472891158467091723047675096941375108772863901566950878383321]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

34701048941540407341643422869169059107051645959827433830930205773767483097576548701936352142446623208590

discriminant (Δ)

1337572783173179776848255698658349775492246884427399113478884052186796269781611471073945492076862079181201098896640000000

Faltings height

21.7488

naive height

284.4510

primes of bad reduction

2, 3, 5, 11, 17, 47, 163, 1440568660837, 4784675273461600689217169, 5556656264356811701028663, 21081150860015766554751539719545661

regulator

46179184335327081845544429474.4229269190898287151133050299427007098835858827092269048431810

submitted by

Ritik Jain

submitted at

2026-10-29 13:48:00 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-29 13:56:05 UTC

Witness: 26 independent points log in to add more points →

(391533298921877893595924687898115934/2996440996419049, 223644142515562745683358874154215677516944481240342761/164024452008816612431093)
(1576037368126584795776667763542783440410436165500936730/8355846481449367640760721639748209, 1895131160222547068659820191349238372785736114939820071950989350082209002865695695/763810595207412607491001497619642632606278212696823)
(18606710500014038857790/121, 2377897295276547242665412238673015/1331)
(-646009235859906693193495210/12952801, -12457253886538546898577220614798999814565/46617130799)
(-4635164927513173690, 230668219996157223043860792965)
(4642391470845585950, -155735269924341613568822502115)
(-379977422247408203978350/6241, -32614867668726160255087322286813565/493039)
(-46690501188838733290, 289270753425647411363679154325)
(51661367443979141210, -119494160188045969135015912675)
(62323052374588535373506870/758641, 382455852384365207398824912817410274115/660776311)
(-164026799245784402545/4, 2512653491460973550513083818745/8)
(88486513810290888070, 673436826666353105788421216965)
(13525734337977621863494982/3481, -49738905204771262543396702536528667841/205379)
(-1532388193527665223394/25, 4073846685339579703106751731281/125)
(198851801917625799923/4, 586907998097591844212478222223/8)
(1871247653935383011330/169, -160017683472934591135378246160395/2197)
(-86331195941264637763870/2809, -48537143699031856289805285185256695/148877)
(1135168731227982754070, -38200250349167668874485132829035)
(57524485414766552870, -219836184610533753637030695835)
(340686526416521358264960428095/151437636, -198791727625050877527085032240141053357533135/1863591548616)
(50683544183682140570, -98334683018745341603529492535)
(55291053407738017670, -184456772761933402787242409035)
(891349635428845183766, -26559720448565139169636838163883)
(39306179591264094950630/529, -5647766389824542410904932541231645/12167)
(-37560289444232712828916503339371956755607379172503843913557786218869793452250/57192190513274710624043379043515143747495437956859628005081, 2762886513693575257689302072972623433141797245316091744836747980314980905337635894286587649857772869196429740357890785/13677448749380745889478889231668223287478504381830553750287870345453739103274642687443229)
(-15093175148743131939753209816286845527195380891895575287967740320/11066355270426247390944122797912195859639002969, -241472652919981624175909517305264050473487451651347088792690982004881245229268057719828143036469895/1164144559344576325122828166147258401045087039971063735028896933280547)

Commentary

No commentary yet.