curve #5990

y² + xy = x³ − 139660314173963196769507676193138239780083896150013152150x + 867316338091391682857256209229192534658783435852710403246028308456490710161042622500

a-invariants: [1, 0, 0, -139660314173963196769507676193138239780083896150013152150, 867316338091391682857256209229192534658783435852710403246028308456490710161042622500]
c-invariants: [6703695080350233444936368457270635509444027015200631303201, -749361316110962413988669364784077892565714238744146341090474411770574014101941772794801]
rank (lower bound): ≥ 30
torsion subgroup: trivial
conductor (N): 8271715155405553481885092585610900195192700182609395052784941335501791096123170191746499494920225747961072781036355100854356282050520760370
discriminant (Δ): -150625862919328013609146641641051887871794029592860010193678788996269082112115005523469500647342829443644655966838483091169549923555826544246883566627950570141721600000000
Faltings height: 31.3591
naive height: 400.0727
primes of bad reduction: 2, 3, 5, 7, 17, 43, 53, 61, 67, 79, 8233, 311123, 30529231, 60992481324017306163967019649383, 660189936915218930224827205442843665070049640700195752604793378353921255341189
regulator: 1020180755256967575516865430362327387.7975531346859294468408098885578601221222085778927168742783583
submitted by: FNacc
submitted at: 2026-10-27 17:00:55 UTC
last updated: 2026-10-27 17:00:55 UTC

Witness: 30 independent points log in to add more points →

(-52288199399376446594904173473638220477486246707376255680886019990624019020488676/6634627873285331235368576843974949430204670426841025, 657102615700602182533526641231672320977478892928050323709941318319193558073717480727328874202477633448930922425735503258/540411837376915481584685510739364288504716175598504668154000855409326044382625)
(3480048700362869101579010892, 650720834632950112685717188058902029746202)
(331432642701554117595016718244/25, 145013465425387814449986913674063822749472762/125)
(8167683111073366613891799300, 521046873054906720839071735553475747062850)
(23489724905620811954169991875/4, -3997472583333935016020032932524643009687825/8)
(48429143558403400623053319950700/3481, -261173057116643188267847629976461284596695004850/205379)
(415864453268449508653477772380/81, 389598643194273547872940259971824538317522250/729)
(9299953370212690379026985749800/121, 28051117094327500595061091435559618493486658350/1331)
(27920343015577732502852833682475/5476, -217383485471913201398941101897729026143050777225/405224)
(88045117570031016883767683117/16, 32972227429790733810341831965336073841866603/64)
(-9062810518378127071841626500, -1178414858727923237428287229867763785261350)
(-23268493900887793227249170791200/6241, -569922037635535790661690069350662032049901401350/493039)
(2442459875475879331896229677180/361, -3304544491536864371273066216346464279288249250/6859)
(5074212739043045735274352061175/676, -8644839866175008409063134529777826313014045275/17576)
(6392352822316189291832119263/4, 6440910108005162717315076040514995280692041/8)
(-1708989129710126543961626466900/169, 2451918208967563924369704638926135978012553250/2197)
(-3380930561857920530994378659700/289, 4661076270869116925700788298871140258689657850/4913)
(-6284263243826155207703472900, 1223438031136417069874502214347840489527850)
(932232854666465558464822735500, 900019544484313754575430491646652169325237850)
(87593466662059818744250421580, 25704181890883683712024624481424145642676250)
(15037113795648161339291728650, 1472189576388873639555278557588728292134750)
(-333547056538321985472686294340/49, 420448626413677648808471305740940601241457350/343)
(38283302283204688354115647685550/841, 229875505959283012086991449149076664298460174900/24389)
(1669971512802283486805587525290, 2158006556708935130712894475523297319882409950)
(249621508357909465806275064300, 124579875192124914180078624914487212411177850)
(56950695829393490101642994490, 13327655910905278296775482679608655660219560)
(368559342572077197560657937217725/35344, 4904789112726596698942637065529722997681833344375/6644672)
(129001176296895197347024907340, 46147575194510846510017113463823254693341210)
(1017345513525307733852482804834700/157609, 30317561932789774231593734572106205883345752426050/62570773)
(85900304591454413611662551300, 24954297714071722762359819757914364858417850)

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