Pairing-friendly curves suitable for cryptography (k=10, ρ=1)

The table below lists ordinary elliptic curves defined over a prime field Fp with 220 < log2(p) < 256. Each curve has prime order N and embedding degree k=10 (i.e. p10 is congruent to 1 mod N and no smaller power of p has this property). These parameters yield a pairing-friendly curve at or above the 110-bit security level (See Freeman, Scott, and Teske, A taxonomy of pairing-friendly curves, 2006).

The data is organized according to the negative fundamental discriminant D satisfying 4p=t2v2D, where N=p+1-t. The endomorphism ring of the corresponding curve is isomorphic to the imaginary quadratic order with discrminant D (the ring of integers of the number field Q[√D], since D is fundamental). Attached to each entry is a file containing a complete list of all such curves (up to isomorphism).

The values of D were obtained using the method of Freeman described in Constructing pairing-friendly curves with embedding degree 10, ANTS VII, (2006). The curves were constructed by computing the Hilbert class polynomial modulo p, using the algorithm described in Computing Hilbert class polynomials with the Chinese Remainder Theorem.

As of 11/29/2008 the table is complete for |D| < 1012. There are 85 non-isogenous curves satisfying the parameters above.

Class GroupCurve Parameters
D = -1,039,452,307 p = 6462310997348816962203124910505252082673338846966431201635262694402825461643 (252 bits)
h(D) = 4,548 t = 160777000809802606072486235096533360383
y2 = x3− 3x + 3758367241838192900521619847487468746423998825048250968622890736520073467386
File EC1039452307.txt
D = -1,227,652,867 p = 18211650803969472064493264347375950045934254696657090420726230043203803 (234 bits)
h(D) = 5,328 t = 269901098952705059670276196260897153
y2 = x3− 3x + 4895448155544427302902823327885395803350583145191176515253483276841682
File EC1227652867.txt
D = -2,307,463,867 p = 594390182450554886611036512830174508087704895899188826533055932991927759323 (249 bits)
h(D) = 4,528 t = 48760237179511540460926726962645450753
y2 = x3− 3x + 79623702817007818176760200505706788415479599029661259017900888784010994117
File EC2307463867.txt
D = -2,968,151,587 p = 21299940147108870116853196464970054841764510783764597243030948496243 (224 bits)
h(D) = 4,668 t = 9230371638695566653571450320531483
y2 = x3− 3x + 8726617780219760386183759149592736527669699473803072356259348637169
File EC2968151587.txt
D = -3,283,578,667 p = 312532865879393486871277830492445390935670975553222508795013719329195815243 (248 bits)
h(D) = 7,781 t = 35357198185342315773061786539878437983
y2 = x3− 3x + 300966389736245126895742450516719710793914377453259071702918810374342218103
File EC3283578667.txt
D = -8,464,566,163 p = 5077208964230286383463597331892147893088142036699711717077705574573523 (232 bits)
h(D) = 10,332 t = 142509072893346497743618821322403403
y2 = x3− 3x + 1819895353689806402460140986310063284251981870481787347073952989497854
File EC8464566163.txt
D = -9,633,854,587 p = 1014460853457197715212715858710978480203340771897273777069008929299226883 (240 bits)
h(D) = 9,304 t = 2014408949004345259650364210520215683
y2 = x3− 3x + 413426036844107627807211113067525477284157185369806722245127304312605388
File EC9633854587.txt
D = -9,652,155,547 p = 58022331069970822060978717638245860257408233964316636604504311113609163 (236 bits)
h(D) = 13,626 t = 481756498949296259770170740633526393
y2 = x3− 3x + 5874579493307857702146294384269504010622599466956880907696567683483825
File EC9652155547.txt
D = -10,867,653,523 p = 8515979268216945232514393674048314616067476694613831667862196492763 (223 bits)
h(D) = 16,480 t = 5836430165166698962381038457275393
y2 = x3− 3x + 6332638262552783415065392805980699470890930791459232701264728709280
File EC10867653523.txt
D = -11,039,933,587 p = 1733497510794069595772386306446050491655700829670808546837857943666763 (231 bits)
h(D) = 11,280 t = 83270583300324481293080121474750393
y2 = x3− 3x + 283619981378153783369107407963961442697314803687662757804457359159493
File EC11039933587.txt
D = -14,590,273,747 p = 74182803082177849643358683333084639059607958432599736928339641078523 (226 bits)
h(D) = 14,986 t = 17225887853132894426211526329150903
y2 = x3− 3x + 61559962862332603588939067316586013284799005376813623618080860642423
File EC14590273747.txt
D = -102,284,409,043 p = 373115547537989111705391053244625577403767798886488797775778287092003 (228 bits)
h(D) = 47,092 t = 38632398193122265016079961798352253
y2 = x3− 3x + 180711824702205677791740256834776749136610521958501567706533251840958
File EC102284409043.txt
D = -15,905,796,307 p = 23424573162748522004326311347604430725366603514263097015425688827297523 (234 bits)
h(D) = 11,988 t = 306101768454535538342108971050547653
y2 = x3− 3x + 19981328082650360589751261379070052227581355228543897848700819252557722
File EC15905796307.txt
D = -17,513,226,283 p = 145123228421472287810807131608081422571855650179376393961519193160083 (227 bits)
h(D) = 14,384 t = 24093420547649292863434924402845483
y2 = x3− 3x + 1888492189442901657063290288351209162236588706194071309833915697439
File EC17513226283.txt
D = -25,858,139,107 p = 98785326044242260993290533311423833671338352502138724402271471758763 (226 bits)
h(D) = 19,492 t = 19878161488854270900478770536344143
y2 = x3− 3x + 91137598755225916565059381348741115749131901339313214147752037621343
File EC25858139107.txt
D = -30,301,687,243 p = 4513473013939617884588558879832221993632732971421004608430988868723 (222 bits)
h(D) = 22,096 t = 4248987179994600964923858203986053
y2 = x3− 3x + 1154514615266589337715825131895879152704725367830285892307490405328
File EC30301687243.txt
D = -35,879,270,443 p = 5826833189144399945222465360945224947990975746712989673313599482226027244123 (252 bits)
h(D) = 19,108 t = 152667392578040710378935400260183340353
y2 = x3− 3x + 2795137314462647963179964483324326562153379334315844535341039327773433113178
File EC35879270443.txt
D = -37,392,761,707 p = 1124398973734561641198702811862311418107901197218686099367759049531603 (230 bits)
h(D) = 21,944 t = 67064117789904957228058111866208053
y2 = x3− 3x + 588419725934082544446010564218534083863700513228001855845943820715818
File EC37392761707.txt
D = -42,206,902,123 p = 35020313330230179546864815519406651568763557582901698518966694217203 (225 bits)
h(D) = 21,168 t = 11835592647642141548437786324118853
y2 = x3− 3x + 21429193165744141193724499123928964252052626259798309439892734808110
File EC42206902123.txt
D = -42,228,067,483 p = 1906285311028986189027657977078833687247007164670345215275857582399357163 (241 bits)
h(D) = 32,880 t = 2761365829461200665291843490587660143
y2 = x3− 3x + 1689585947323021358476145459142375418693482789791695720860518971496082556
File EC42228067483.txt
D = -43,171,313,563 p = 259033959846562394650489477708619709768296650347852787128996718630003 (228 bits)
h(D) = 25,152 t = 32189063971887246827239695753221253
y2 = x3− 3x + 50119449885945144761156434130585051318959452198832457482049575460940
File EC43171313563.txt
D = -43,211,683,483 p = 54984284451644153054476797953984456787622129247610547932694512257796531643 (245 bits)
h(D) = 27,974 t = 14830277738686373375235977775647811633
y2 = x3− 3x + 36075200407907835721304809273836294289172255697510466515566821010338263088
File EC43211683483.txt
D = -47,224,437,643 p = 1722552449207734111767131364383940147214073042673617159711899061683 (221 bits)
h(D) = 21,976 t = 2624920912490686155733547021645883
y2 = x3− 3x + 972803419136800720544097657787139116279797062123027688842752443776
File EC47224437643.txt
D = -62,270,945,707 p = 571648550709346198478382885459231759169445159734441973438000037275803 (229 bits)
h(D) = 36,050 t = 47818345881443711790637196734653153
y2 = x3− 3x + 483639776860576735069421072880850625749821998933370370114049816467476
File EC62270945707.txt
D = -63,485,071,747 p = 6770130791774694540848516935471264461040561798527220129756300439923 (223 bits)
h(D) = 35,531 t = 5203894999622761235886942247752453
y2 = x3− 3x + 4733399178162931934378892264423999340487221381403530647679479110581
File EC63485071747.txt
D = -75,864,433,243 p = 11669108718073601694910611061194256404415641292633876545797582073644323 (233 bits)
h(D) = 26,065 t = 216047297766702943735067975214608253
y2 = x3− 3x + 7106948829367962651737217758206119854739779065878759286358810013215810
File EC75864433243.txt
D = -81,426,169,267 p = 7741381306413655884576577977915034877150140837226432761313422377397843 (233 bits)
h(D) = 35,414 t = 175970239602197006096198680961145333
y2 = x3− 3x + 3496840493291993750415270070813697736669412436800958628056358879097852
File EC81426169267.txt
D = -92,945,701,267 p = 58606251523528374674193413199102033192584135646535151269446839596016083 (236 bits)
h(D) = 40,624 t = 484174561593350852797807791352055733
y2 = x3− 3x + 7898404637013009073947532342975789552687993895880208281311583420143554
File EC92945701267.txt
D = -99,043,620,043 p = 19630401391769267528040326131052100554213998175439712660835701413395590067443 (254 bits)
h(D) = 34,472 t = 280217068657633827072373503698125812933
y2 = x3− 3x + 14717520906005012089897487183809343212697421396987293064119483998558902964523
File EC99043620043.txt
D = -102,284,409,043 p = 373115547537989111705391053244625577403767798886488797775778287092003 (228 bits)
h(D) = 47,092 t = 38632398193122265016079961798352253
y2 = x3− 3x + 180711824702205677791740256834776749136610521958501567706533251840958
File EC102284409043.txt
D = -105,920,458,843 p = 43347667453850334470701560503377719332401171969216299671443430279203 (225 bits)
h(D) = 54,872 t = 13167789101265304586371498246323603
y2 = x3− 3x + 40087867782445752672073394874588137894702721112527743015099277908797
File EC105920458843.txt
D = -107,779,055,827 p = 5791699700393784469732722495658852018150030162940219349475523600025883 (232 bits)
h(D) = 33,672 t = 152206434823154365476257661289190433
y2 = x3− 3x + 44009738400649256338864306594059948728119402564135023042610424326312
File EC107779055827.txt
D = -110,865,016,507 p = 19337286979901395377379596880284035576219206054231444708922990270429894083 (244 bits)
h(D) = 43,416 t = 8794836435068339661197673951502176483
y2 = x3− 3x + 7198967943664093960789714607735987467278881167785447886906429662284281021
File EC110865016507.txt
D = -114,389,133,307 p = 379380559503386907314797180195655619756944860617093891154685963315563 (228 bits)
h(D) = 28,144 t = 38955387791851689244289768726304393
y2 = x3− 3x + 319845625182418100785550901270093150939497674702416615399008369689985
File EC114389133307.txt
D = -123,677,762,323 p = 14619344973611650157138907992043442980596385841349066612643579521683 (224 bits)
h(D) = 40,454 t = 7647050404858503391382811911642133
y2 = x3− 3x + 3333938547352895528949557264574302813476139037846696035208836040595
File EC123677762323.txt
D = -123,677,762,323 p = 14619344973611650157138907992043442980596385841349066612643579521683 (224 bits)
h(D) = 40,454 t = 7647050404858503391382811911642133
y2 = x3− 3x + 3333938547352895528949557264574302813476139037846696035208836040595
File EC123677762323.txt
D = -124,985,532,427 p = 817902885968941719784749597952730386054609587934063609102014874413201763 (239 bits)
h(D) = 45,304 t = 1808759670015827967664368552415406643
y2 = x3− 3x + 799598078191747383432245635170341054512760799371908067841060056164297537
File EC124985532427.txt
D = -137,486,872,147 p = 123833391117752481091068869949072840074409811015358309384867101554153029323 (247 bits)
h(D) = 56,089 t = 22256090502849100437387197596405609503
y2 = x3− 3x + 62303478856929163494194821480893697935827888108316571785101216042978691805
File EC137486872147.txt
D = -144,666,443,803 p = 3571015157999358401809172641247223454264338200138540045417207405326463083 (242 bits)
h(D) = 52,908 t = 3779425965936815861315471833429159983
y2 = x3− 3x + 2433707345656945719831653803616538914488993741304066882243776157139099001
File EC144666443803.txt
D = -172,449,579,883 p = 6720677564558220637886530649017805270034715317415693542645762983803 (222 bits)
h(D) = 56,800 t = 5184853928340979072557379852587153
y2 = x3− 3x + 2104680364267836483525225219849964465961386930123903314018252251050
File EC172449579883.txt
D = -218,603,020,483 p = 16150741302827059458025692963269741853095705546192858990041235957994643 (234 bits)
h(D) = 55,072 t = 254171133709766966983488294935795883
y2 = x3− 3x + 8863823807067945544990377429260787336294815940302866101930907736288003
File EC218603020483.txt
D = -222,790,745,323 p = 12385486559960774683397767517205972542964559570182085095689790404951443 (233 bits)
h(D) = 60,324 t = 222580201814633771199539191920400683
y2 = x3− 3x + 1490991679926715342246535570799387284793110651181301420240258255198583
File EC222790745323.txt
D = -222,932,121,523 p = 1455854386722415743432230938564311712461743802948391722229266779203963 (230 bits)
h(D) = 49,920 t = 76311319913166637441135148107633143
y2 = x3− 3x + 472301085329579443974382360533227486773998045818042691986795561376409
File EC222932121523.txt
D = -235,455,188,323 p = 27307021806142337221300937934849547803425870941775752134400671191280846283 (244 bits)
h(D) = 76,188 t = 10451224197411963895985784175585722783
y2 = x3− 3x + 12437816496394582693354714324347013119477906365904005796107820124697587288
File EC235455188323.txt
D = -258,618,421,483 p = 99473739894528479421778655690686622222686462531902235341341951899003 (226 bits)
h(D) = 57,132 t = 19947304569242279399019084668580753
y2 = x3− 3x + 86404537425747994048161127426025998695817596551770244698366351011896
File EC258618421483.txt
D = -259,056,933,307 p = 56494592886078272119498878017518736740647765103289424219620409252283 (226 bits)
h(D) = 70,615 t = 15032577009425665619046965124741783
y2 = x3− 3x + 28398891479300826042764954985422291221027963377465808832614460285106
File EC259056933307.txt
D = -271,913,410,027 p = 109202931065046352122692945796807442252631437434406408498222480826483443 (236 bits)
h(D) = 85,902 t = 660917335421144335178777866474068933
y2 = x3− 3x + 83018638958170029587209794220887042129646804568485675449373475533873706
File EC271913410027.txt
D = -272,507,658,283 p = 69418170813692184541763997830310236049281462557998080495799925847245553764843 (256 bits)
h(D) = 72,900 t = 526946565843984543721948430653206233583
y2 = x3− 3x + 37906072963014418761012579067545315520242634797471123730841164525068988335311
File EC272507658283.txt
D = -281,228,280,283 p = 5625941063904877003826677872997566596597892360434310314437320142603 (222 bits)
h(D) = 64,802 t = 4743813261040057847283915974202303
y2 = x3− 3x + 4172162620331889690438401999823097963781860452270216552348292385938
File EC281228280283.txt
D = -296,857,273,747 p = 4033223007307908340732774595289268647377945445318910196629747046443 (222 bits)
h(D) = 58,816 t = 4016577153402089618937966199139433
y2 = x3− 3x + 505888442922429911238796460532791336693405654817522435103764242295
File EC296857273747.txt
D = -322,147,410,427 p = 972129487835059736013181504947748083848823215863216880051140746327204403 (240 bits)
h(D) = 77,284 t = 1971932542289476733015172595299118203
y2 = x3− 3x + 83285233964038854772473945984406762317855230635230329807281250755358903
File EC322147410427.txt
D = -325,953,507,883 p = 2125150705618281758702971559377348238684487292767400006244802495778727443 (241 bits)
h(D) = 87,356 t = 2915579328790956947371090934164216683
y2 = x3− 3x + 479550921268198749025673547595516301286736350107766396709795362112588276
File EC325953507883.txt
D = -341,023,950,523 p = 13760715237706312932092722191600240471707617556531268885433918206509456083 (243 bits)
h(D) = 62,136 t = 7419087609054448396483945883171015733
y2 = x3− 3x + 8364951930236562148432524027839623988551161791139424905949478369661230518
File EC341023950523.txt
D = -357,641,057,107 p = 18506495854708158345125653688354677726348572280364787146233817434228603 (234 bits)
h(D) = 76,720 t = 272077164456763319489521518098321553
y2 = x3− 3x + 14718845823242107534119781762429039474094161859692410123673278009697761
File EC357641057107.txt
D = -371,905,000,603 p = 1482246579793442264178706755589884283977050278485854284917898391084141203 (240 bits)
h(D) = 74,937 t = 2434950989070163822034510785883634603
y2 = x3− 3x + 394897554492053946966176773359660280141666802576204437172346185104993483
File EC371905000603.txt
D = -378,408,782,107 p = 207293158527594215399158906325170740994232674535983323404719427719990843 (237 bits)
h(D) = 78,539 t = 910589168676180148202364753188954583
y2 = x3− 3x + 48936027826535385154598200574970139319510277739152990928823590125960384
File EC378408782107.txt
D = -394,604,625,187 p = 5372837842372728584492078760175292139698950479201964233907736788123 (222 bits)
h(D) = 79,812 t = 4635876548128834107377929772848353
y2 = x3− 3x + 5226869086865269713344408372381521750245829515763661349393999850786
File EC394604625187.txt
D = -397,614,252,523 p = 99039034681221118740164317693588354144005907344408508868900461484386963 (236 bits)
h(D) = 85,693 t = 629409357036328524076372691352271893
y2 = x3− 3x + 45646967194391345014882598057509764781415529945181760976355758089421834
File EC397614252523.txt
D = -403,043,622,763 p = 1345262081927661505061607650390505474160391764595858835122239418394631603 (240 bits)
h(D) = 75,240 t = 2319708673025698289753682832280758053
y2 = x3− 3x + 953050278865996244692555675734414245016429684539034021237831067631756920
File EC403043622763.txt
D = -404,316,355,243 p = 2349945239496305284484281065992622470942809156487376507705857812363 (221 bits)
h(D) = 94,376 t = 3065906221329220816181764405990143
y2 = x3− 3x + 1320395203042932572051661344591951581710054371056110926099660658604
File EC404316355243.txt
D = -405,854,131,147 p = 40431763031420548379495252173002867749635036111185671162035322523043 (225 bits)
h(D) = 93,504 t = 12717195135944175387621334219993533
y2 = x3− 3x + 18167923887212208432919892351327561947250970642920882167131838137940
File EC405854131147.txt
D = -426,147,664,123 p = 1228162206741180816935675958888323022122845366218175511068998286907923 (230 bits)
h(D) = 92,978 t = 70090290532745855267003157865252203
y2 = x3− 3x + 55541393935851162233187700020856262937097885906632389336364781515211
File EC426147664123.txt
D = -436,970,847,523 p = 23008031558769161324736279254117232999220701872363505787849325861982688760443 (254 bits)
h(D) = 72,904 t = 303367971669846263780844385703644988433
y2 = x3− 3x + 7212494310457240293486422120225317153124357733206481314782549570819618467934
File EC436970847523.txt
D = -438,182,716,867 p = 296341449095803745748149156554902621073663753529100568232517444733042776163 (248 bits)
h(D) = 86,170 t = 34429141673634778300289021014786142643
y2 = x3− 3x + 4713134641905453849387759631172409853450667689681595900848561149306400320
File EC438182716867.txt
D = -457,423,133,443 p = 172739559214667455884225457177537777635616439961227237482604830731226723 (237 bits)
h(D) = 106,609 t = 831238976984759674314856846025377053
y2 = x3− 3x + 17107564441751852052171505911682612624752418025878261315331056262507859
File EC457423133443.txt
D = -459,099,167,827 p = 15737341718409696705520416581099358187938541497707087785944179915923 (224 bits)
h(D) = 95,207 t = 7934063704914322580869315423794453
y2 = x3− 3x + 8896531465962274700531657349408021344978657117505682097005692744977
File EC459099167827.txt
D = -485,742,948,667 p = 73285257460388840128772508291555212452367967324217684946499023777362363 (236 bits)
h(D) = 68,658 t = 541424999276497538894245945366521393
y2 = x3− 3x + 411055974246392130919794645026921941563612283119600219364343994402347
File EC485742948667.txt
D = -529,167,219,067 p = 2067496171175939157148079920166934790905929277653010135178179141212749363 (241 bits)
h(D) = 92,393 t = 2875758106083290974923428120585473893
y2 = x3− 3x + 271279754320517853215947924980035952630685359609939810212052497451807548
File EC529167219067.txt
D = -546,354,937,363 p = 2618562851303387688743963969292328588437182369636832120844443378463806311683 (251 bits)
h(D) = 80,390 t = 102343790262104084118231819271653770883
y2 = x3− 3x + 225695761917800943895818198936057251121331801087342614180460273457212999934
File EC546354937363.txt
D = -548,774,355,643 p = 22688574729139276962710743558516589870224307644853387735247953732421267958723 (254 bits)
h(D) = 101,890 t = 301254541735982974459415759545243384803
y2 = x3− 3x + 13607786670290435310099687327073611396365355474786695538541777637331024519465
File EC548774355643.txt
D = -561,060,287,923 p = 26951534931441333452775293421795803203230264882563362431689535908652987599683 (254 bits)
h(D) = 60,960 t = 328338453011165498198556270436532222883
y2 = x3− 3x + 4744297900063161509975017296289324778562145029704744299245963409049479087965
File EC561060287923.txt
D = -606,064,670,707 p = 10641290153419156186288795730575822028910366371003227229163620352804523 (233 bits)
h(D) = 121,128 t = 206313258453441679786632582658794153
y2 = x3− 3x + 4724976695011432340574037118606879387324574922914198707062928273036706
File EC606064670707.txt
D = -628,084,895,707 p = 1649854992835483232446547504299136553160389111324055112438691761203 (220 bits)
h(D) = 90,664 t = 2568933625328208617044060280244603
y2 = x3− 3x + 456580484931553907872047636620089937709251391892768916020831743093
File EC628084895707.txt
D = -639,477,214,003 p = 1201474366826483015910237518291311421935196422498813759911072112963 (220 bits)
h(D) = 112,959 t = 2192235723480924407965607671786893
y2 = x3− 3x + 1062042759881228936913419527059844596516325877548124146721438794512
File EC639477214003.txt
D = -652,190,124,667 p = 32073772717846584102546881551331913213062127941625263012990282996885429924203 (255 bits)
h(D) = 101,104 t = 358183041015883855609365979636523977353
y2 = x3− 3x + 25466266592813693589500495845476932747873988665882763684385308838442827421021
File EC652190124667.txt
D = -660,489,903,187 p = 302262812709621203750994807270566463869104102066351771918533502296763 (228 bits)
h(D) = 92,316 t = 34771414277226125146214283455625393
y2 = x3− 3x + 226796684631625311944244855641516134670390705825375397813321189714448
File EC660489903187.txt
D = -674,576,925,883 p = 6065742729259736209424054740882870971874547592875394266040624897643 (222 bits)
h(D) = 106,398 t = 4925745721922615123746153308282633
y2 = x3− 3x + 5187934530188537031693414930438986356241744464101315790783621724504
File EC674576925883.txt
D = -690,090,276,307 p = 28744660496855370448798022511716619003612467449078003886993185433262763 (235 bits)
h(D) = 121,283 t = 339085007022459608181212883952744143
y2 = x3− 3x + 4811922283601951915835331806807405631179783406077728775582967875446432
File EC690090276307.txt
D = -711,513,888,067 p = 55119432595102147161500602790032422743141768096963905478576500705988563 (235 bits)
h(D) = 101,403 t = 469550562112759682559263623189171893
y2 = x3− 3x + 5220709457302630142997211413791528553211101355249052293917196793777192
File EC711513888067.txt
D = -730,369,058,827 p = 8195166215739810158128324004332511835383370256099492034161234135852866163 (243 bits)
h(D) = 74,256 t = 5725440145784360623762845609943967643
y2 = x3− 3x + 8048611609801043331192426632292393842026588377397990163885488926656158518
File EC730369058827.txt
D = -735,125,631,667 p = 16752735121037973135375806839864671936692721718440715218199987395402206083 (244 bits)
h(D) = 82,384 t = 8186021041027923753079347088833890733
y2 = x3− 3x + 3028569280766715622928877780551404174708195869100159368348414648476743733
File EC735125631667.txt
D = -757,552,418,827 p = 4613681274536157609291679661717696718103563946417185427672319659123 (222 bits)
h(D) = 106,708 t = 4295896309054098949640615260776603
y2 = x3− 3x + 4417539299847335023529686473663798270029775249108257024271891027154
File EC757552418827.txt
D = -776,648,522,203 p = 21052121363128012011938410462958894270158773990198869855874998004883 (224 bits)
h(D) = 103,810 t = 9176518155188930265496649431878933
y2 = x3− 3x + 5067289727980049531145576758511937294724485441908079574739431971000
File EC776648522203.txt
D = -951,784,972,387 p = 244073911198776883337204347754766057619245553707476310839164739359963 (228 bits)
h(D) = 131,880 t = 31245730024998736350917078459623143
y2 = x3− 3x + 236080845440076401331231062665590854997803053505195711932019271136797
File EC951784972387.txt
D = -955,087,079,467 p = 21948381506099619580154987572031483607726236109625573767155685681958168026163 (254 bits)
h(D) = 145,688 t = 296299723294502045879213486914200673893
y2 = x3− 3x + 7290077661197659516837535970362724135450555987479020732692531898072960171140
File EC955087079467.txt
D = -1,882,359,901,387 p = 109855417317614207294022189107239380145543996394873521691477923195182984195043 (256 bits)
h(D) = 188,448 t = 662888881540833228943229306406029485533
y2 = x3− 3x + 94758013886579422163155941665968137032960821154449367171747667767405735466296
File EC1882359901387.txt