curve #3850

y² + xy = x³ − 244137883624250098833250921072060802985605625x + 1536502644033473414217070054192897523387664308713787892321652248057

a-invariants

[1, 0, 0, -244137883624250098833250921072060802985605625, 1536502644033473414217070054192897523387664308713787892321652248057]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

751841644675185779513791129152734054336617046719891649837010943151012480351509643708134877277781214861524932521279310

discriminant (Δ)

-88591839640623401245988333166201350950923643922525678126465316444243128373199263509966865365664825722269182463976444487870513600000000

Faltings height

24.4601

naive height

318.3234

primes of bad reduction

2, 3, 5, 11, 23, 37379, 737119, 53689907, 359923640091095966296988914704687676219, 186044267761389593070215345567303068591394032815108748673

regulator

91397814264940001289082536310547.93874869171943066286587571077229427751259502293040859532704030

submitted by

Ritik Jain

submitted at

2026-10-04 00:07:29 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-04 00:15:15 UTC

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

(1761041071245687695094119662442056491406223377872703694874/181344409880103845238765023445563881, -22041170908563304020391398132951790259041476164497533598057796556883861580833260063633/77224705158151222441533275177695499508040504645047029)
(201613289696340729635184, 90263368236684469447027946557079013)
(119403590150839655220591/4, -36527853325199344155968844723449991/8)
(4227680150685788598290144/361, 3652330542449963887320139234726409657/6859)
(10227802282037186631354, -330783861939240571435040610265677)
(-802600304529378596594904/49, 366365186686615187951947348634847789/343)
(13660941830153294503745898/289, 48041182808749856080170250368945218259/4913)
(1716059542685326434522441561/222784, -35346291501678879836743963232590241802471/105154048)
(303747801192636866837129034/22201, -2878769799119191206813186625085022914313/3307949)
(40101997867178389655497794/361, -251569530056430001613658162166302165543/6859)
(24958104289170749214098634/121, -124338603437447578252617966892396377687/1331)
(436995230813810562372294186/2809, 9090817557623387808590391481667567515671/148877)
(1286267590066922280020839851/1444, 46124390385764983589196873987796303346481/54872)
(-16185776345970834448206, 1117015919206505527317281464273443)
(22787238736056137042504, -2793874745929424636657760921752227)
(218761975516803571427277/16, -55590407609764249533417505466726415/64)
(-1227888142686686896312046865812734806/76100656097761, -749637971610557061644500219224666693768300218165876493/663869324414088829009)
(2036479086123233061386580253129700374311347225964/158497509048437587477656601, 1440044167084870032282703266748301498735871786595658111904981834982011453/1995416972220773549894544230934231819901)
(15831709048742756428343122286136783096708056041783316668391329512282101975471956914/1771936179650236802771555240474766698327860868255278062026041, 617108606702014917962967590548588160452901913604134134291434451738323492863067918234056174495021467359436110883136140695047/2358696776828385046463915646487265069946809901834212919039780789837090029323377868717780589)
(12262998818092843130572964851305423705292067674226/1605969047981755586537157649, 22062592126818247611482200696815007817937467320330834844934462380243906101/64358476698384965559954862852592547433607)
(-67899929339488835700603462523411836434600823968727205779509186/3777476412009512121821500111275882179241, 79477340483970805986721425066816266970293637763347218165388925009299565118489944522094048153/232168150483108338732607791731726180877042466592156588975211)
(10182497366276975085351199249426044855144858/1291824139070120688769, 14819260803011836648451243052283231919218641800230165278074785779/46430685251351926692910937756353)
(-2527839195406211355594205024696628482484530917803054/139393016571312194079489764049, 231050606564465236883356865522593437686315370260297860655361940320592709611/52042904328002921670706413219016954659477657)
(-17346258436052135168161982348840490054013734226892450388678148810374906061971524147227069/1092080713273458524612239339715789774248756896410715775547627891524, 1353719785412792457663812640946798474589643884130843666637850791825794543676230611486806122235401966792672131418743263928605990971859/1141253456670001182339333080831014699527062294304405242367421597119748981325277529824754501633901768)
(145142363399087475401693154491974898951949278528476646443752719847822730255357075117016454/15134247169701227524343511590985585876889545516800443723684414879681, 16359247340788490626385524869520422998747665425571553076365764789238395450915932792721940192043100659312070636364140258283796846355173/58876398179637449976639260411059915979575268653430457909976346365369447217162342903593734196685784671)
(-1336161384823929298936863193505845858797014129586110280519855114149133500415910248575044989/142338717435200229836142982525120411940270650283080626290589239964100, 2941868351494231075153822512674114704303452605672807550785938185602926434037896678313092675654487060283581008299721597696157096265342661/1698183326004115983690728104345437041289340565581300374053786742956316122369672279413389209831367811000)
(147169953975308117391836069114560100066591897913120049236758043/15874179385861281813148434444497185065316, 528994308407225381206966522669088406521316043251489791103111293880405894731991351021662305821/2000031913792958444173552299445931223905490702301593477498136)
(8471850539772670040062568190930599854767744/1199936469745352507281, 16871944873155954148567329963407494812449914875072404390815918797/41565918296479414331623109476679)

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