Torsion group Z/10Z, rank = 3


Dujella (2001)

y2 + xy = x3 - 662057554395863819655x 
           + 6555937806015269208934798118025

	Torsion points: 

 O, [15204607110, -67941800897355], [14508246060, -66888206628705],
 [7767913230, -1371809902183875], [23282395290, -1939686489026055],
 [23282395290, 1939663206630765], [15204607110, 67926596290245],
 [7767913230, 1371802134270645], [14508246060, 66873698382645],
 [-29710565514, 14855282757]
 
	Independent points of infinite order:

P1 = [6528464250, 1584915470789805]
P2 = [-1251382860, -2717068690242585]
P3 = [234157109127026470/3122289, 
     107363591829490639800339875/5517084663]

Dujella (2001)

y2 + xy = x3 - 4281263352573652971565x 
	   + 107821663654697042219512111579217

	Torsion points: 

O, [151106661871/4, -151106661871/8], [38658903974, -298124191759837],
[38658903974, 298085532855863], [37778521874, 553359104063],
[37778521874, -591137625937], [19466574194, 5644185762393983],
[37738137374, -13037357834437], [37738137374, 12999619697063],
[19466574194, -5644205228968177] 

	Independent points of infinite order: 

P1 = [38884390274, 374658605091263]
P2 = [68144084374, 11511432778916563]
P3 = [63596755816498/1681, 1295465435236059911/68921]

Dujella (2001)

y2 + xy = x3 - 194893737997038726814052934940x 
	   + 33116538928063906147760473209688087642871600

	Torsion points: 

O, [254754441578780, -3513286725747626740],
[155923053598730, 2553216176076833653760],
[1019524782879295/4, -1019524782879295/8],
[258559200504980, 101940657731359903760],
[254885906826230, -121678567430089990],
[254885906826230, 121423681523263760],
[258559200504980, -101940916290560408740],
[254754441578780, 3513031971306047960],
[155923053598730, -2553216331999887252490]  

	Independent points of infinite order: 

P1 = [20645366256649420/81, 6181433476946512840/729]
P2 = [366203161320830, 3294756456379543927760]
P3 = [6763257201404423015251311798240171890/30430663076172557016361, 
     4686465337444992434378968860543553400778455713416972160/
     5308442572234136882937273541037141]

Dujella (2001)

y2 + xy = x3 - 489947814397230700269047753x 
	   + 4173986155348349327100911472235093494297

	Torsion points: 

O, [50821743663663/4, -50821743663663/8],
[18672290044426, -39188206919547108605], [18672290044426, 39188188247257064179]
[12982660805878, 1174990135682956555], [12982660805878, -1175003118343762433]
[-7723858718018, 86588016541465379419], [11756274291562, -6233765322000803261]
[-7723858718018, -86588008817606661401], [11756274291562, 6233753565726511699]

	Independent points of infinite order: 

P1 = [1210503846669361840932/193237801,
     98719822627082311300356878237469/2686198671701]
P2 = [11716484125164953506/641601, 18647683095020784752143426699/513922401]
P3 = [406163047331649294562/31550689,
     63512630297765411472994259035/177220220113] 

Dujella (2001)

y2 + xy = x3 - 1065792807399105888102105x 
	   - 14138522318461624729140413052612423

	Torsion points:

O, [-13267924006, 6633962003], 
[1192775315994, 641549883979002003], [1192775315994, -641551076754317997]
[3843399621594, 7256940917155203603], [3843399621594, -7256944760554825197]
[-289481697006, 519740967164688003], [-896540313126, 469854104209178643]
[-896540313126, -469853207668865517], [-289481697006, -519740677682990997]

	Independent points of infinite order: 

P1 = [3250496816394, 5555659957899356403]
P2 = [186533412086244, 2547582657528201264003]
P3 = [525289619690230026/182329, 355310265239928169781449449/77854483]

Dujella (2001)

y2 + xy = x3 - 184412619490429624603376436635x
	   + 30449869006658311731557296945588399421430225

	Torsion points:

O, [241399646091870, -120699823045935],
[261551664901870, 330152418666287954065], 
[261551664901870, -330152680217952855935],
[470634689151970, 6921204132746982815065],
[470634689151970, -6921204603381671967035],
[199559393560870, 1263266348110425395065],
[-234545329000640, 7797454476683252627575],
[-234545329000640, -7797454242137923626935],
[199559393560870, -1263266547669818955935]

	Independent points of infinite order:

P1 = [-1116794535560755430/22201, -20816234916764614772949826615/3307949]
P2 = [125853840882825662670/1042441, 
     3356524891621704135156972742965/1064332261]
P3 = [981601603524680197854529/834516544,
     915120379740248722266702111911541259/24107513923072]

Dujella (2001)

y2 + xy = x3 - 1720200171313840213498718405x
	   - 3751937785045595550204425248421402406975 

	Torsion points:

O, [48890378542210, -170317335580283576105],
[-40338426667790, 20169213333895],
[-4908547052750, -67627506573466181945],
[-24420189561290, -153924652688932355105],
[158261820685810, -1920405983267376707705],
[158261820685810, 1920405825005556021895],
[48890378542210, 170317286689905033895],
[-24420189561290, 153924677109121916395],
[-4908547052750, 67627511482013234695]

	Independent points of infinite order:

P1 = [8732856352345330, -816074068024243690346105]
P2 = [435045913630802142/10201, 21929693359406092588790967/1030301] 
P3 = [-1178704981454444510/80089, 3072547107159783254014685365/22665187]

Rathbun (2003)

y2 + xy = x3 - 10596063090767790103x 
           + 20246425576229652155786091497

	Torsion points:

O, [10660983062, 1057809698659349], 
[3063510998, 128593280399765], [1234385882, 95118461651849],
[-1465751194, 180634502985845], [-3962951978, 1981475989], 
[-1465751194, -180633037234651], [1234385882, -95119696037731], 
[3063510998, -128596343910763], [10660983062, -1057820359642411]

	Independent points of infinite order:

P1 = [76999022, 139395067572389]
P2 = [-1803119302, -183001883318563] 
P3 = [-9954485811022618/2588881, -268032218567773557918019/4165509529]

Rathbun (2003)

y2 + xy = x3 - 15875150677713173875x 
           + 24822054816914290733556790625

	Torsion points:

O, [6482435150, 440810876209625], 
[2656504910, 37370358331865], [1980656990, 33895148327225], 
[-292649650, 171589331512025], [-4610716594, 2305358297], 
[-292649650, -171589038862375], [1980656990, -33897128984215], 
[2656504910, -37373014836775], [6482435150, -440817358644775]

	Independent points of infinite order:

P1 = [642290510, 122026581035225]
P2 = [172849001273/64, 20776308116988049/512] 
P3 = [5193847730, 287188032457025]

Rathbun (2003)

y2 + xy = x3 - 92677956255664016180x 
           + 299418090541143369157794628752

	Torsion points:

O, [1190849074, -436740106860842], 
[7866118444, -239011952852072], [-8179534256, 714308411013028], 
[22077982264, 3002472582804988], [3843260968, -1921630484], 
[22077982264, -3002494660787252], [-8179534256, -714300231478772], 
[7866118444, 239004086733628], [1190849074, 436738916011768]

	Independent points of infinite order:

P1 = [1384052854, 416890415479138]
P2 = [16854993713896/1849, 36614073002814544516/79507] 
P3 = [-31232439846128/5329, -311521602654411394748/389017]

Rathbun (2003)

y2 + xy = x3 - 255845251297258429380x 
           + 1656026164827548903395128129552

	Torsion points:

O, [30856178784, 4810379926953468], 
[11347840344, 462634572184428], [7465457694, 402609054032778], 
[-2811437556, 1533982175210028], [-18574240056, 9287120028], 
[-2811437556, -1533979363772472], [7465457694, -402616519490472], 
[11347840344, -462645920024772], [30856178784, -4810410783132252]

	Independent points of infinite order:

P1 = [-63488808, -1293162455707332]
P2 = [-18555573606, -120509508651522] 
P3 = [94325517211656/169, 915729403935302259276/2197]

Rathbun (2003)

y2 + xy = x3 - 66668901366044310944470x 
           + 6625719732081856769026747158085412

	Torsion points:

O, [148993766924, -53522427505702], 
[149076537164, -1969149062182], [89869949864, 36878583765742718], 
[151332026204, 1513981122546458], [149073495628, -74536747814], 
[151332026204, -1514132454572662], [89869949864, -36878673635692582], 
[149076537164, 1820072525018], [148993766924, 53373433738778]

	Independent points of infinite order:

P1 = [1848170969068/9, 1078216082430740030/27]
P2 = [2743563893303564/1681, 142006313746134666811018/68921] 
P3 = [1017670335636899916836459780176268/6778938733428979045681, 
     391836738288044475865952612598693870267434913046/
     558139248511289461872926040243671]

Rathbun (2003)

y2 + xy = x3 - 333848836163677156595x 
           + 23118493712440422090809079478881

	Torsion points:

O, [148277045254, 56865096858614161], 
[36395104798, 7692648382380793], [8491176460, 4571203342778761], 
[-16817037614, 4896616359342253], [-32372614898, 16186307449], 
[-16817037614, -4896599542304639], [8491176460, -4571211833955221], 
[36395104798, -7692684777485591], [148277045254, -56865245135659415]

	Independent points of infinite order:

P1 = [29709174118, 6278717358451369]
P2 = [-3028247394408758/106929, -109791324853798192416781/34965783] 
P3 = [-20222528897455117220/1730310409, 
     -362916327837846171969380434387/71975722083173]

Rathbun (2003)

y2 + xy = x3 - 1139407008286275015150x 
           + 4292069755092734127597502522500

	Torsion points:

O, [-6104308140, -3319620265808310], 
[36165309900, -3222865110114750], [-30055759950, 3374475194761350], 
[114272212800, 36963058325032350], [3815690300, -1907845150], 
[114272212800, -36963172597245150], [-30055759950, -3374445139001400], 
[36165309900, 3222828944804850], [-6104308140, 3319626370116450]

	Independent points of infinite order:

P1 = [-32516929000, -2638219862445850]
P2 = [74384137104564450/1369, 20287119188878733936485800/50653] 
P3 = [86742979800, 23624955623054850]

Rathbun (2003)

y2 + xy = x3 - 2706794767207398160775x 
           + 104036717500887330936430796523657

	Torsion points:

O, [199799974054, 86828697615339973], 
[54738736054, 10949194874871973], [19080776374, 7702965541524133],
[-27178198346, 12550998610129573], [-65531503946, 32765751973], 
[-27178198346, -12550971431931227], [19080776374, -7702984622300507], 
[54738736054, -10949249613608027], [199799974054, -86828897415314027]

	Independent points of infinite order:

P1 = [12082890934, 8549547651801253]
P2 = [38947494828286/49, 242567093115030121579/343] 
P3 = [1519521249241436901034/316448521, 
     59229051536758204828502259789437/5629302740069]

Rathbun (2003)

y2 + xy = x3 - 85367971368866370224970x 
           + 9600329958761086926144205117637412

	Torsion points:

O, [631745385924, 455851087460469798], 
[224002906164, 41442833641353318], [177215981364, 6108786589295718], 
[170086545204, 945392262521958], [169127032628, -84563516314], 
[170086545204, -945562349067162], [177215981364, -6108963805277082], 
[224002906164, -41443057644259482], [631745385924, -455851719205855722]

	Independent points of infinite order:

P1 = [146601221364, 15362951610935718]
P2 = [56905918813679219488776489/151913118692416, 
     325306579707736365878791552403549806887/1872375369472109694464] 
P3 = [96508987742246211949072385592/416995227452521, 
     29981356635497501660225358545379694291287690/8515234779380334432181]

Rathbun (2003)

y2 + xy = x3 - 2868129375368734318380x 
           + 56353767705358492933999767345552

	Torsion points:

O, [-9326148216, -9071445418980252], 
[39302992344, 2083252730094228], [22639945944, 1738944202331028], 
[101054281944, -28257440648100972], [-61515958056, 30757979028], 
[101054281944, 28257339593819028], [22639945944, -1738966842276972], 
[39302992344, -2083292033086572], [-9326148216, 9071454745128468]

	Independent points of infinite order:

P1 = [10720966872, 5180429592265620]
P2 = [1882741944, 7138660979279028]
P3 = [2343190105641/64, 332731274056480761/512]

Rathbun (2003)

y2 + xy = x3 - 26807678961979361599180x 
           + 1671973481886398199216900733380752

	Torsion points:

O, [888030698144, 823507677766192628], 
[240726282344, 95752385344073828], [135263153594, 22818198562595078], 
[108081934844, 6093295672313828], [102267872344, -51133936172], 
[108081934844, -6093403754248672], [135263153594, -22818333825748672], 
[240726282344, -95752626070356172], [888030698144, -823508565796890772]

	Independent points of infinite order:

P1 = [25884341468374/121, 100722806369203064318/1331]
P2 = [1361808057962889832/4870849, 1361095593766655035862613788/10749963743]
P3 = [51016257797402488328/1153349521, 
     937381582801799984507863640996/39168903082681]

Rathbun (2003)

y2 + xy = x3 + 18102609072937378371095x 
           + 2391315383141885864187311821586777

	Torsion points:

O, [949839828644, 936229893979266803], 
[217748396894, 129063950086167803], [48024969314, 58064227520336723], 
[-49624126006, 37024167548117603], [-90776305606, 45388152803], 
[-49624126006, -37024117923991597], [48024969314, -58064275545306037], 
[217748396894, -129064167834564697], [949839828644, -936230843819095447]

	Independent points of infinite order:

P1 = [-87018262856, -12535506208626947]
P2 = [513146707222814/1681, 13142663455928799782563/68921]
P3 = [-45811830943919866/516961, -3549341061576412485995423/371694959]

Rathbun (2003)

y2 + xy = x3 - 1072509749585005340703485x 
           + 427513459352382138507725842537962225

	Torsion points:

O, [1685047150810, 1845203675439914215], 
[700476245170, 141231423321407215], [609714290320, 15847413174326215], 
[599321700070, 1831862037273715], [598242577570, -299121288785], 
[599321700070, -1832461358973785], [609714290320, -15848022888616535], 
[700476245170, -141232123797652385], [1685047150810, -1845205360487065025]

	Independent points of infinite order:

P1 = [43806710477602314328/18003049, 267082543841383277041350540349/76386936907]
P2 = [-992152721110320832310/3029071369, 
     -143765053846529113732474509645925/166711000935653]
P3 = [532198552387045624317507142839104944471445739430/888781210181180408156315747995117969, 
     917092949578682197451636864032880764153538672188479485117341955228305/
     837900205329316833742346751713820715453665076473023047]

Rathbun (2003)

y2 + xy = x3 - 883386649322495701946465x 
           + 319496253706806704712837565584338121

	Torsion points:

O, [472836276850, -86677601425546061], 
[559261410106, -19345595033594837], [-425132819636, 786266892279582091], 
[897336196078, 499346659568304079], [535622962602, -267811481301], 
[897336196078, -499347556904500157], [-425132819636, -786266467146762455], 
[559261410106, 19345035772184731], [472836276850, 86677128589269211]

	Independent points of infinite order:

P1 = [923422235134, 539598911257448035]
P2 = [1265858243273134/2209, 3957357675610324296353/103823]
P3 = [5623099856733941638/11992369, 3800403463396504157613701953/41529573847]

Rathbun (2003)

y2 + xy = x3 - 578032640617033128241903x 
           + 168987816077776276363859737591053497

	Torsion points:

O, [354870041822, -92472377442045931], 
[462441823958, -23993149080307555], [-412063127908, 580695542956764269], 
[827619715946, 507422848787929745], [427743075782, -213871537891], 
[827619715946, -507423676407645691], [-412063127908, -580695130893636361], 
[462441823958, 23992686638483597], [354870041822, 92472022572004109]

	Independent points of infinite order:

P1 = [414918855542, 24137568977415389]
P2 = [42468784175672, 276716836050073032869]
P3 = [730611006350059703475636166/1420365067928361, 
     4714938399116980835597864208519845010095/53530336601880796638891]

Rathbun (2003)

y2 + xy = x3 - 494272503533200381660985x 
           + 132893239202578155784198210732683897

	Torsion points:

O, [271190070034, -137098135330462517], 
[453570966634, -44913528763095917], [-469279817816, 511369849893950683], 
[965030437534, 744729259818884983], [379061621338, -189530810669], 
[965030437534, -744730224849322517], [-469279817816, -511369380614132867], 
[453570966634, 44913075192129283], [271190070034, 137097864140392483]

	Independent points of infinite order:

P1 = [13333866418350886/16129, 1101706034236993487249989/2048383]
P2 = [54370606829471706/124609, 758670409981598324883891/43986977]
P3 = [4694892336701935390378/30238079881, 
     1286827926598908104084852021554241/5258129948586971]

Rathbun (2003)

y2 + xy = x3 - 15325167875235731315350450x 
           + 23091703604460609373920789898685034116

	Torsion points:

O, [3487446996740, 3472939753539243134], 
[2307197462276, 122867543937109118], [2262122720564, 5072324104146446], 
[2260255719428, 209333176199294], [2260181346052, -1130090673026], 
[2260255719428, -211593431918722], [2262122720564, -5074586226867010], 
[2307197462276, -122869851134571394], [3487446996740, -3472943240986239874]

	Independent points of infinite order:

P1 = [77879905120064521796/40056241, 203629328363079386881286653102/253515949289]
P2 = [73196114392468886856548/1688634649, 
     19724938692728179133509815910076038/69391063631357]
P3 = [428085016334277869001881769701089410876884/9065900384331594613571986225, 
     279154917788487378073866612864510646089872490498549588731628782/
     863209903109579807119314925210780149411625]

Rathbun (2003)

y2 + xy = x3 + 192796122563125780368450x 
           + 155909350241595531287647769098776132

	Torsion points:

O, [3507818764164, 6632884885021574058], 
[808754647404, 916966143330134898], [168255649254, 439444677255394998], 
[-236657510496, 311493738427033998], [-421170712996, 210585356498], 
[-236657510496, -311493501769523502], [168255649254, -439444845511044252], 
[808754647404, -916966952084782302], [3507818764164, -6632888392840338222]

	Independent points of infinite order:

P1 = [-2235437621475684/5329, -13577640508208784297534/389017]
P2 = [-6563367046446208196895114/17768863687969, 
     -13871657044343452221125672285189397354/74901322099123669297]
P3 = [33261764081430725032478384312429530656/254365028362998992122425625, 
     1737135501914033296063645895307920908229269565852060488746/
     4056823399097871207147470251834702671875]

Rathbun (2003)

y2 + xy = x3 - 7649243335383073965811655x 
           + 8142795550383366515479921899421152777

	Torsion points:

O, [5607542507644, 11898564071547668053], 
[2053730226394, 1046685535270043053], [1663129993294, 146044986191326453], 
[1606965253894, 21298269816338053], [1599791163894, -799895581947], 
[1606965253894, -21299876781591947], [1663129993294, -146046649321319747], 
[2053730226394, -1046687589000269447], [5607542507644, -11898569679090175697]

	Independent points of infinite order:

P1 = [1600431707644, 4514321257268053]
P2 = [1602500041714, 10635144525625873]
P3 = [78837975718070756866/6932689, 
     680985123836895324840312597461/18253770137]

Dujella (2005)

y2 + xy = x3 - 40831178941372542828065222070x 
           + 3175629333206587210466338025198789238575556

	Torsion points:

O, [465215339181983/4, -465215339181983/8], 
[157781537176938, -813140072400800683992], [157781537176938, 813139914619263507054], 
[117773943758376, -19688075661400169322], [117773943758376, 19687957887456410946], 
[110241951843390, -118838833098688209036], [-54726329163216, 2290472925613647419346], 
[-54726329163216, -2290472870887318256130], [110241951843390, 118838722856736365646]

	Independent points of infinite order:

P1 = [112662024425394, 74127591495502625166]
P2 = [20231332765150776/169, 124969135011225177512670/2197]
P3 = [248886292340818383/2116, 1618592576503357055893119/97336]
 

Dujella (2005)

y2 + xy = x3 - 3167417955766446777616642470003x 
           + 2169731181079804686115895249944813736109996897

	Torsion points:

O, [1028154118808462, -514077059404231], 
[1030174366001778, 142986412430918688705], [1212296521936926, 10561655507654855860329], 
[1212296521936926, -10561656719951377797255], [1030174366001778, -142987442605284690483], 
[1049250402097752, 1209996117079378246119], [2951047671053622, 136096532596926808677129], 
[2951047671053622, -136096535547974479730751], [1049250402097752, -1209997166329780343871]

	Independent points of infinite order:

P1 = [9266412390358954/9, 2968242966904450017323/27]
P2 = [403778104293132324267731/388641796, 4860545641493396128491075164585555/7661684366344]
P3 = [6520074015413231830275412733639212/5909509097602379721, 
     61190425985854807375390278556652060333546915014231/14365710438695529224855275269]

Dujella (2005)

y2 + xy = x3 - 14160511348505020530242089048319085x 
           + 648583081924884489422144357690310684311298281049297

	Torsion points:

O, [69003372881528514, 131203519896793021308063], 
[84881244665194434, 7627307885852590927732383], [84881244665194434, -7627307970733835592926817], 
[-18876236921122446, -30152187527912573732838657], [66573602916759234, -961249207578287083570017], 
[-18876236921122446, 30152187546788810653961103], [66573602916759234, 961249141004684166810783], 
[68622632259372738, -34311316129686369], [69003372881528514, -131203588900165902836577]

	Independent points of infinite order:

P1 = [91320903775662677556242/1555009, 8567258309690234922128237970906673/1939096223]
P2 = [18942233649606180601773779132631/237733164285604, 
     18743277203672268287493979635186078073425137871/3665512091387685263192]
P3 = [3034801337589873317300864753365734216499168283442/42307481769541122508826763202609, 
     380997704306416185608090500601993179461021753393520834679570511112324887/275185637834082845614665336359288299276879287977]

Dujella (2006)

y2 + xy = x3 - 17872399539372964708236646896139510x 
           + 919649651172241073723029335429666977203870924072100

	Torsion points:

O, [308738504436059039/4, -308738504436059039/8], 
[77184628635132620, -1236780537791346310], [77232656061117620, -23114453065829525871310], 
[77184280329867620, 166367622420839753690], [70610207655852620, 3118378125398762298293690], 
[70610207655852620, -3118378196008969954146310], [77184280329867620, -166444806701169621310], 
[77184628635132620, 1159595909156213690], [77232656061117620, 23114375833173464753690]

	Independent points of infinite order:

P1 = [113263590664242620, 18664818323928735933503690]
P2 = [73099539110282253312295897880/947073473329, 12673737245861541299429202929474997770/921670121553896233]     
P3 = [3298757670805004277852010/41254929, 356041144555318865565047209218847090/264980408967]   

Dujella (2006)

y2 + xy = x3 - 241674368637382436130973196439385370x 
           + 45729241997248669057664305104858534991896264733452900

	Torsion points:

O, [283827619337213140, -141913809668606570], 
[284804581878173140, 902008425100717608033430], [283827908802733540, -258354253302585094970], 
[283827908802733540, 258070425393782361430], [284804581878173140, -902008709905299486206570], 
[283811097217008760, -15254661247734420494990], [228064527019301140, 49742430337787415444345430], 
[283811097217008760, 15254377436637203486230], [228064527019301140, -49742430565851942463646570]

	Independent points of infinite order:

P1 = [281388466189995640, 2247531347057661990993430]
P2 = [3792810840651454000753017700/14964384241, 50380138896345475438585006249200030158470/1830578159817289]    
P3 = [973668208940655607987704058900/3430492961281, 807178624692949282133240627874963320170/6353818412673255679]  

Dujella (2006)

y2 + xy = x3 - 11021417385938715332603261187894955x 
           + 445352851144395353746731567265819211866421289871025

	Torsion points:

O, [-1023883331071690, 21369052934972669064848345], 
[60695061667093310, -34712740020738770826655], [59816038578440510, 338563914411535305730145], 
[60594965644053310, -30297482822026655], [68513295869053310, -3441735765048914797026655], 
[68513295869053310, 3441735696535618927973345], [60695061667093310, 34712679325677103733345], 
[59816038578440510, -338563974227573884170655], [-1023883331071690, -21369052933948785733776655]

	Independent points of infinite order:

P1 = [12465074529838037440/121, 26727283965781025762863517915/1331]
P2 = [197362312008760012965600686750/2792805409, 87679054346047469560500152338568126681996335/147591387449423]  
P3 = [7279860000102634788037293654382091349288590/119648721640899198102598489, 
     129033596312999870021054550871158305470046193004499101202552765/1308766271828219336158964843799348502237]  

Dujella (2006)

y2 + xy = x3 - 38875889469082213659860930876707285x 
           + 2950316463860325033045384057841591682836609405168097

	Torsion points:

O, [113940507718716434, -60040997449360005918217], 
[7188152804511434, 51684059806945676446496783], [112727434442902034, 646666984605054519867383], 
[125942934649610834, -7199456935245733986467017], [125942934649610834, 7199456809302799336856183], 
[113940507718716434, 60040883508852287201783], [112727434442902034, -646667097332488962769417], 
[7188152804511434, -51684059814133829251008217], [113816638297963538, -56908319148981769]

	Independent points of infinite order:

P1 = [84950117860335938, 16150836175292900655793751]
P2 = [-34119999775758233133653374/190633249, -170064689234686698704283970923093661111/2632073268943]
P3 = [121570467310812872851585737298651724/860011038331575601, 
     13334803949103178814177187581412024104613227441787503/797546545453279973964623401]     

Dujella (2006)

y2 + xy = x3 - 71257460691961675173754316523320370x 
           + 7321390120337424024246609088090663066342591280763012

	Torsion points:

O, [-8015742362007036, 88837247474479955213419518], 
[151823965812582924, 1555855907262811837739478], [151823965812582924, -1555856059086777650322402], 
[-8015742362007036, -88837247466464212851412482], [154065224310056964, -77032612155028482], 
[154368657019319364, 166312644394631247945918], [176008550745896964, 15232805839753172605291518], 
[176008550745896964, -15232806015761723351188482], [154368657019319364, -166312798763288267265282]

	Independent points of infinite order:

P1 = [565897425112079083044/3721, 313487097535584725080273087158/226981]
P2 = [381662697015232613357860899/2406294916, 362234760560965741181926595054602905477/118038390809464]
P3 = [1022273400893140482593904664548/1241270059129, 984929546973308861615650762035046601912881050/1382927522086978867]    

Dujella (2006)

y2 + xy = x3 - 4238819163950333612296472587853300x 
           + 106220970522341035586146111878778198927882318975632

	Torsion points:

O, [50349955394968504, -4521027931276388488109252], 
[35626477581489454, 652330711897084269230698], [-16935180628906496, -13158614018286746783234252], 
[50349955394968504, 4521027880926433093140748], [37921994976441004, -106145718898450014629252], 
[37921994976441004, 106145680976455038188248], [37483023338718504, -18741511669359252], 
[35626477581489454, -652330747523561850720152], [-16935180628906496, 13158614035221927412140748]

	Independent points of infinite order:

P1 = [52598459480241004, 5365109675503022071770748]
P2 = [11386837739738465147336974/327284281, 5488187059489077001036733642975022958/5920899927571]
P3 = [495853421966934580421465164/3977951041, 9764349642399898070864959668938141641928/250893350106911]   

Dujella (2006)

y2 + xy = x3 - 220359657496467741418150313873591015x 
           + 39814921951574944336532299033911263640999340112193225

	Torsion points:

O, [270816100429600630, -135408050214800315], 
[324318677092538230, -49606979822935602075536315], [324318677092538230, 49606979498616924982998085], 
[271855156972960630, -727728837240255818000315], [271855156972960630, 727728565385098845039685], 
[-52146824856430730, -226194995513372069242932155], [264543940064404630, 5815475515295121402759685], 
[264543940064404630, -5815475779839061467164315], [-52146824856430730, 226194995565518894099362885]

	Independent points of infinite order:

P1 = [45626454289284532720/169, 2025062418036112881114791695/2197]
P2 = [47813516951160931710665830/139736041, 110509836262490288318628102954671531785/1651819740661]
P3 = [-26386122583162159892375556671690/51589986968689, 
     -50709454036154035911544421438941429495752276595/370551117431084079113]  

Dujella (2006)

y2 + xy = x3 - 1829791340653224667774114991260030x 
           + 30126481652601492426131833796965804347432944395076

	Torsion points:

O, [98611768400657183/4, -98611768400657183/8], 
[31597344905782268, -1963791351963980011997902], [31597344905782268, 1963791320366635106215634], 
[24847002476702876, -39158154824457032356942], [24847002476702876, 39158129977454555654066], 
[-8783446032243556, 6746904608084263758516146], [23718566855425340, -264229789668437098231246], 
[23718566855425340, 264229765949870242805906], [-8783446032243556, -6746904599300817726272590]

	Independent points of infinite order:

P1 = [-26185984518095269783/1024, -254233324676475203287785567941/32768]
P2 = [66341418779904786303192614876/2694243202225, 70792055663019156398833666405919002118654/4422371205780148375]
P3 = [3538295972881588182892789262554811/15495486995956900, 
     207015376560826646116842621903629502005116893781349/1928891702330401394503000]  

Dujella (2008)

y2 + xy = x3 - 78495183659714260569230485446839778x 
           + 5272104352807515304061804334811509687856386729800772

	Torsion points:

O, [-249582843133818348, 96520681499430631158452814], 
[-12933452548430568, 79278967287136183705915854], [-249582843133818348, -96520681249847788024634466], 
[-12933452548430568, -79278967274202731157485286], [287599720998302943/4, -287599720998302943/8], 
[267824530150038708, -58823605770453272381840130], [814371604401805296, -693858781237529230113433566], 
[814371604401805296, 693858780423157625711628270], [267824530150038708, 58823605502628742231801422]

	Independent points of infinite order:

P1 = [26905083000245500697198910102804600156/38109524548662000625, 
      129231298831152382588579508838210724768673275439902465254/235261193485177213949257015625]
P2 = [61089994062969540332174951906751450791115336/156777029010923424547615081, 
      361164280318356859510509894669634451734406422359914688472536013554/1963015122063684646944903524705914228021]
P3 = [251987439926933604515814172885394133558380170782/1013663390482789098698972779489, 
      34172780721022020782576171613275674988774580421758766731741921047779680/1020564935200664946695843626286255613092313263]

Dujella (2008)

y2 + xy = x3 - 2707084078782823399463620124873144405x 
           + 1702941498964699709396875520306791902694958494215053025

	Torsion points:

O, [838252747503423310, -150777770893893676923719105], 
[-1898447295304972014, 949223647652486007], [45873975438784210, -1256524304845457629141412105], 
[838252747503423310, 150777770055640929420295795], [45873975438784210, 1256524304799583653702627895], 
[1063229977901742610, -163172832458654714397562505], [1063229977901742610, 163172831395424736495819895], 
[2270216825346754210, 2694013516618984399895517895], [2270216825346754210, -2694013518889201225242272105]

	Independent points of infinite order:

P1 = [-9222522812219858510/9, -49792379587455274006495781635/27]
P2 = [-634376402773896638959710/413449, -398269099977964027763935852971893235/265847707]
P3 = [730817967871035095096236969096489751544550/54640731806117262803761, 
      620239691235355355514699216073263334217062911426845560825980995/12772466164302796378973199146131241]

Dujella (2008)

y2 + xy = x3 - 5207948535449509181956620222384153276635x 
           + 141731197956455666679691319855852979111513623376407070170961

	Torsion points:

O, [49593773618723283358, -73670654680072313752108553807], 
[146904257962504960783/4, -146904257962504960783/8], [22408636891743128974, 190474670820835661791531209505], 
[-53541525876671066210, 516803139599795962381500035761], [49593773618723283358, 73670654630478540133385270449], 
[117853563723184375726, 1079295397457421748303848017473], [117853563723184375726, -1079295397575275312027032393199], 
[-53541525876671066210, -516803139546254436504828969551], [22408636891743128974, -190474670843244298683274338479]

	Independent points of infinite order:

P1 = [-39865331034157693964, -534782224368394300690522260527]
P2 = [33345598889978869465534100386/945870025, 1283133825472785724024352659311193345627619/29090232618875]
P3 = [643268314919899950976556302319854/702637915225, 
      16265788218548020443810910513269212047485993312947/588975692868627875]

High rank curves with prescribed torsion Andrej Dujella home page