curve #390

y² = x³ − 3430010766159976165957759077669961926755875x + 2681763916740340149774032713047940546291901244757804845784121650

a-invariants: [0, 0, 0, -3430010766159976165957759077669961926755875, 2681763916740340149774032713047940546291901244757804845784121650]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 527802750706022069032532367959662152467996623758456834729754016672150261043328308280093916020742761409186800
naive height: 305.6218 ★ record for rank ≥ 26
Faltings height: 23.4349 ★ record for rank ≥ 26
discriminant (Δ): -524227361283301111952687109986788365790975204436997531101690296581897343456825488147499036358295585145566910976207347955573120000 ★ record for rank ≥ 26
primes of bad reduction: 2, 5, 13, 17, 29, 41, 47, 73, 101, 107, 773, 2213, 51630402754009, 1533363917498289404397862460817511362700420516712999862115622234114028919
regulator: 64631143695357006727043332189.6982095126509640060000207750864136230853585717484607697884217
submitted by: wgxli
submitted at: 2026-08-27 13:21:39 UTC
last updated: 2026-08-27 13:21:39 UTC

Witness: 26 independent points

(300204299052072467888733325043100111908086748351490/782978309793680374551277205161, -26135421464673865996672178797766152309981897458621182482192880114889784115170/692826669538929715028606588954787829196309909)
(21490000651881915068318929/34596, -180958368170969069481741390955945169183/6434856)
(1662070906567359700798489/2304, -2669856273703520926482763640854272637/110592)
(23763806260116393767392394061/16265089, -1842737931316139178411639728224725030644384/65597103937)
(15336329526445042915505/4, 1713803737110739325122217826145615/8)
(20933735266442652150865, 3017364235065206812715697280938620)
(12743810780566213941762731/21025, 87587785909910011017954422162912367754/3048625)
(48442418372971922667806, -10654332068979114694120070855686996)
(680737286222862705034126608853754062525/294329761334545561, -13474397230258321224790778531087819592534000057188795982320/159680273355589325110261309)
(-31672061409989361886503056440682750/15085059834601, -1468309440648280079310396942178816582227769111752770/58589603059538719349)
(10654545595029430432257940164063151925/22141989670611409, -111375300275503729973038322591806232838339631120054891040/3294768959241899278472423)
(1092217857284796790934951114662766/25362011117041, 6429689147673860663434247738418200900327767070473864/127724888688207785911)
(688160751146395019335711194800930/1683565935529, -80203925312499119112286822306617574870202654962010/2184465523365394667)
(10224855351840641117046896978735247596869/14766595456735961721, -1434077571550531079496542697573485703278496223634989763902928/56744080868362811068926727731)
(208694110424206104323950/81, 76275731701967193792478177285556080/729)
(29995016252441078022400820214308369/56723416935025, -13616324915040950210178264642812671542542892773363972/427212131029056112375)
(6608566204770353462401, 518296436293733652064044764036324)
(15127463512121466861217010111916645/190630911769, -1860081728847779380567666420933058745529465551838960/83231934280198397)
(137257123359884713841979552435990465829/5433681409093081, -1603866622005627348878961155464993293768961241017693385008/400535723452315508131229)
(1692885637091852958195909370688696739305/39050278057090624, 69590813273110937010611253976227417415245171606922159917835/7716781366859855962413568)
(2533853557035696234447229/1369, -2619247220814514725178103832696796592/50653)
(3134014508261149555130232755331021/31981957225, -175418157683764804930413646872102743359790882243056/5719493320332875)
(36801859839250393423759016896112565/27681309257809, -3162494197627101508359920286979095845055007646711840/145639755442038265127)
(142149168378439024615606277433322435/96750692733249, -27148596601171120347056471898310193008549525642445590/951658486607934681057)
(6760078103653674872602151127962868634850/17499083377378201, 555805179559023595164622128710543959776064050140809660688270/2314850512900519056282301)
(3207389880527800559639218178090714130/160203876465889, -5720508261875521157684208466068471904352142430523369390/2027727218476126876463)

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