curve #636

y² = x³ + x² − 845145340258227325067785179435620730242899736479927779088145x + 288637782452890275902427430227145504558805052503286048161223316808921460136463218344804243

a-invariants: [0, 1, 0, -845145340258227325067785179435620730242899736479927779088145, 288637782452890275902427430227145504558805052503286048161223316808921460136463218344804243]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 670680596092887981338516472522940222263082784098629608755433259352759553349251817529360901286443176028756432959132459902554234845450997536315090686840
discriminant (Δ): 2643716123846282846080077335611042964565944537621509734369611356655257687853699028377103987837194680901781273551447755822244221874453124611223968477857615810483534748092157076000000
Faltings height: 33.3866
naive height: 425.5742
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 47, 53, 61, 73, 97, 18701, 11977573390704566629, 8464353505545258900460492038712368257344698074836184256100606393685587475217605029226166366189762996119817839
regulator: 202939947242385487175191883039397202.3707612164010613299903295609180306997437495903705925312077
submitted by: 7fff-zip
submitted at: 2026-09-07 23:05:41 UTC
last updated: 2026-09-07 23:05:41 UTC

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

(1531485639254247178669749749806, 1608207127062212040339291410594558132477258625)
(332570576891014179501637625151, 210596000269893669807362556650270002178901990)
(444644166226870752392808551401, -27545223433730271459271469719217275510341990)
(65102442084046008485992647042769/49, -421637243346180551438447761826874922841411317650/343)
(-693093488314806049909695602069, 735836426310198799193332526197466945325486750)
(-269918385510716672741237982194, 705048148647521128193554918115356349997620625)
(878554922240822019637360680193039/1369, 5206628167387941482839309672666213046470543308750/50653)
(24307514686788982753406204165509/4, -118541139918069713129111539914952709001019391415/8)
(421871965714583192877220483711, -84721441334160315976658966912724521668802790)
(101643590369837307760890671311, 451424742623363475951877353865928120699512410)
(742121076625890020875525771810291/961, 9254894289003173391193467021847356328834753020450/29791)
(9966511401016974987388459134721/16, -3990089340827405845633735231760667417560661225/64)
(626438114087177603699864248291, 70967070637575057071167605978166973198794530)
(72264457308098660137638474931, 477431868498268992029610943462512504608958750)
(189585905996293501363110306980391, -2610381456698632183874839789501588296469707646170)
(609772077377632330630587300991, 4291581127816519215078220996197112410521370)
(624228717495062942586082936531, -65663413375291258204977608779797141137604450)
(46741588040924743135091996186131920691/2785561, 319091867470413618428261447830011827311319547052925535450/4649101309)
(13103797966295592370742015830059766509443134/2836586903089, 46556695036184706322641816374394021585117149476143958470805110225/4777427884159846313)
(212479743493781147918330437303454563914454783/22828242407881, -3082662922120712440173787530894950378374308722909900689700758865982/109070853946432958971)
(2037500327411646910117402497345514245130956861889539/3256127469758783432569, -12881507510932702056928896120008333239032434384492943853230690360139658372550/185802732758234117767161496753997)
(377752079906668946554614808831, 152598566796773330532236199597559968938744550)
(3450494283095392322920357928813345446384209271/5073890834100001, 60904835484586901922399793128422306785187391537906941596354568692230/361419581402594862131249)
(579194732126415998594250399932698680016269733159/1359274805657224569, -121550201756422322039552464018312774381650602944640714378256333552663470/1584750512525334059714897997)
(6995216996257814701464000013018249521442606943221/9104238484615640356, 8371600592137419059610623359001504056304183506944627191567761656369654495/27470428777995657790519251496)
(511097642197095015602323149812833122098835219049/834931520424532129, -19742790591556297642047062629138468503955755346001373361625676652671450/762915231025531440829653617)
(1191341678890200816492426602931679/1849, -8556063734583337085766020353775151450020321302290/79507)
(278757279488534796361979853642566926/776161, -121228486880890680953355217710870516132937900747939455/683797841)

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