curve #692

y² + xy = x³ − 221982474188104873848280218124589202489003900511731460x + 35925615261202957969383858360316701469452926338836855861411584007977988750083600

a-invariants: [1, 0, 0, -221982474188104873848280218124589202489003900511731460, 35925615261202957969383858360316701469452926338836855861411584007977988750083600]
rank (lower bound): ≥ 29
torsion subgroup: trivial
conductor (N): 22014470639738362676251328545465262413755634598442843440808339701034183247046310353433809313268420736489040701105578416068371557870
discriminant (Δ): 142500519226947856498079018874640804322776709906404620547800788415257455882357448565140746632701614431939543789208704526364468597811552207495065314874696601600000
Faltings height: 29.6539
naive height: 380.1169
primes of bad reduction: 2, 3, 5, 11, 13, 37, 59, 83, 89, 173, 3221, 34129, 16732804179544737501098553216679331500422814433627865352408496937610200097281793693450091962495166543474060899
regulator: 17780540850789994898040629808930891.8088740905455111804469204920081503790205047032297121081319668
submitted by: wgxli
submitted at: 2026-09-10 04:53:10 UTC
last updated: 2026-09-10 04:53:10 UTC

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

(-2252495312740764752552843032606800209745833838350200/4723353384262330237985041, 59266967926595687030851710850642392678686106069474556800259890363737257557340/10265394847612683878617624795014759161)
(7351120943852409644225880952855/1764, -19808244250918179720830741232266105712703429255/74088)
(31025624557079850422179697400608340320/80252657521, -63852153107752547086034755426831224956701806382832467940/22734695096466569)
(7801817888283987434086816880/49, 737078225236717868227843653948201652270820/343)
(2141910834830027953712494322092619451077180/3315183130951129, 2431047876348144536662860280570863273479885983027007321134705220/190880377750596260790883)
(68795343087692861437235197502486886366273236828/357675582140002602529, 3973546826793421214874079007377542770871851368148603178590084677884088/6764472553662400650622979718833)
(1476429495572194440474794965480074325985522024/4264365904373969689, 6661894126187145288632669117525579156432783908791700925152921599436/8806061079903806934508879613)
(2770285583453397477841165243054675486760/193347551072809, -15385100436903534025439950470591743834629376800883661637879180/2688487450247202286123)
(-100301855715072904388577880, 7561863945118012648347314059462820298140)
(-185297093466750558499477499206680425578/500993580481, 2911946836356115520034554823159056038900490282815411657874/354607765206676129)
(9448304187580098424065416392818930905204/180247728855769, -11961869502906551985265855649921233830379983287942850459285124/2419940577691979949853)
(2727805807403063060370834752225990154856700/7954589780889049, -254869308626136664400486517703770304386438832392595404239589820/709457986354951412959843)
(16757945002140487348590142198/49, 32814187110652871492157589280196018183838/343)
(496810121501735826092952190626476177450264/791456405137225, 267117911055355925668014662067742407282298610885643377838711268/22265912455418703282875)
(1969358546527805907507366647243993342946632/2410150042971841, 2366741978901265065231374166429384237984716326106549749437224324/118322168491478579356639)
(43494845094935948612959626121165814246/51184990081, 248607763957275450734503479139356167511520392705302061592/11580143340915521)
(1774142514364631985011947035889677980/4795147009, -699881731373934861575781612578300557445505659283823480/332049544932223)
(303621109281407458032479775220899515560266316790849192/74706214969360422211974961, -166217851762746840676521285652289884178314583317330540627106175841378220400866788/645706413102291348007777085757112352041)
(5217432142019686052632190036388283701320/13856120309161, 123439941372113560888449550441189642124527736695520678271340/51577758972535032341)
(196660820322646195379797388596904068760/333840128521, 2019223405393384081950750551616755956160036128745420678060/192889154018020069)
(756964971049250111762370508068170124193828368694130/61760106032133375798409, -20811184710209207543233387488218360665613675752320763516116958332131366344270/15348362554110410516992256599412827)
(10594969458673493336920027578742482252501371342145504230/24737616070593025146903038929, 17144284967597506164007540461259907939570282638798494095514537201029570878671185170/3890780830107947039265297320454190609643033)
(3180036742990196716532773255194285552306018710/2916115684568388481, 164458310869310422971501934474531206653146019867032203351804869357650/4979745217394696794456184129)
(394090634906247429233222908178920597307671352312720/55688532973816251891001, 7806414649738155761028837113415302579149217011849538309795379025542407286260/13141612761329034653289378166788499)
(227475199330685373133696095291370728030930187146976520/218173747332752251894442521, -98692500330227380633880810270505602373187504079462357202670630959044286568228660/3222580216691427791256760509797045517181)
(177152040658310347492237012902858101262309872/336867084061545361, -1571732259123147637760277611972951317962030086120987465989801330612/195518504157505678557164359)
(46287888623455195902025854605123753484658528297880/2601001172694132181009, -314811208887228971911076470925628052807627869548171257516134663138910931380/132651089711111223695896685060473)
(376178732187463676517780127216295909894769726940220/989642281089051346801801, -2503963471404071831709494135382942053687949754725348809934181700631793997540/984503722232646578031827056629488549)
(660176390757541076295997887281245959452514898/1518026752082492089, -8700269406603311634099284873630297697954169893727962302938115805566/1870333866360871857344559187)

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