Torsion group Z/3Z, rank = 13


Eroshkin (2007)

y2 + xy = x3 - 560715933702165990261993692150795879540x 
         + 5299428030171662962897867758309003693598430128674403539600

	Torsion points:

O, [8593602267036083080, 33399039471607927923677923660],
[8593602267036083080, -33399039480201530190714006740]

	Independent points of infinite order:

P1 = [30978765264695144680, 132887030666136666891811891660]
P2 = [42714959134973152720, 243484714136201166251098454860]
P3 = [17517044808100174120, 29195754303760059255051062860]
P4 = [14407536544275712180, 14545360491234198754332073660]
P5 = [27024189809840210680, 99410687206608213450615379660]
P6 = [15223373261754620200, 17072594325815595384787766860]
P7 = [-19625425810319741720, 93513850432355415588023731660]
P8 = [18799275311571587070, 37447008534737807545137468570]
P9 = [-18348119874544858160, 97008001583008247645310994660]
P10 = [16004432727240519730, 20612929621400491642269765910]
P11 = [-27235206268166134070, 19202914916421997002398631160]
P12 = [13326569619771689680, 13920236659741078875971506660]
P13 = [27069452184006616180, 99781951498337473669562238160]

Eroshkin (2007)

y2 + xy = x3 - 73262771788012628080963454016709537315x 
         + 240598790801630018163569184912325717758514948008409652225

	Torsion points:

O, [5896914810510119630, 3692079207152305353879997385],
[5896914810510119630, -3692079213049220164390117015]

	Independent points of infinite order:

P1 = [4457502222769039370, 1611641339515815829274369045]
P2 = [4198800350419611170, 2647181824163160663752575085]
P3 = [4663784697212755040, 598710342059502067618068575]
P4 = [4600449196285678970, 960025506026782647465074945]
P5 = [4554776706911186990, 1181769967892808613450633385]
P6 = [2380239538380692222, 8927552162407067648923077497]
P7 = [23702110592754993710, 108718564570356475210335730985]
P8 = [4305435373222259510, 2231488968639382184715604505]
P9 = [4618909929490933310, 863707409335431200909470985]
P10 = [4372416906624676220, 1963518441135919270046813945]
P11 = [36249530734715794730, 212644711673400126644106584885]
P12 = [4693924773486814190, 360230832576196960473000425]
P13 = [4450103380274798480, 1642908737129617992291509135]

Eroshkin (2007)

y2 + xy = x3 - 7032750154590180472810630714591592198580x 
         + 234825110521164672374627005794918283861649641835073217760400

	Torsion points:

O, [30796046079264381960, 217832673380546979749336183820],
[30796046079264381960, -217832673411343025828600565780]

	Independent points of infinite order:

P1 = [55900848433614700560, 127957972604422146757975646220]
P2 = [60064561238865449310, 170599150318472748808550606970]
P3 = [69812369394041538000, 290002371439954245595102699020]
P4 = [61612368528157270560, 188165990173054207603274843220]
P5 = [3822294292797501180, 456069855621822797983703355720]
P6 = [52372587674097006360, 100766688720822135191405667420]
P7 = [51554975084878426920, 96335957098298726629044580620]
P8 = [51147073430501124120, 94458713634598078961223670620]
P9 = [68932207591190829072, 278538666893854221091708241892]
P10 = [47727681973487919720, 88818038537044422433497220620]
P11 = [53338169456226155160, 107033016967755131766827494620]
P12 = [64102710537148435560, 217749619349148168747134366220]
P13 = [52406676754698809160, 100969677496651189732961320620]

Eroshkin (2008)

y2 + xy = x3 - 245159698188178088219881294961406816115x 
         + 1510191009902655798002552220643158891490617937867360088417

	Torsion points:


O, [6148183244268310574, 15339705160042210643860741913], 
[6148183244268310574, -15339705166190393888129052487]

	Independent points of infinite order:

P1 = [10833013559463040274, 11210358084599745780316885613]
P2 = [10706258660637427034, 10613283545662027955006055473]
P3 = [10395143048176178894, 9220066684034404984174781273]
P4 = [10137602529625035794, 8167669882323985109476036973]
P5 = [10038848157700788524, 7795499127400476443202567113]
P6 = [10824343292658261344, 11169050746067025317933688623]
P7 = [-4069189724279614606, -49400540986606610630851023667]
P8 = [-7414688387566494706, -54040095999701376974332025767]
P9 = [-976881606269713816, -41818067551922275505813314057]
P10 = [11184169214867230724, 12932997956751474213414498713]
P11 = [10145221804179288974, 8197181181207665106642796313]
P12 = [-8725386066273219586, -54635334476631791259074142967]
P13 = [13085600454673829294, -23298390072192192872367107527]

Eroshkin (2009)

y2 + xy = x3 - 35822192130572784206480514296239908919425x 
         + 2609719568750620065454923921391767461604324824175741297455625

	Torsion points:


O, [104605984638686332650, 84532082161048799807719188075], 
[104605984638686332650, -84532082265654784446405520725]

	Independent points of infinite order:

P1 = [111765301087195517610, 46430435456204326675146597675]
P2 = [111116582336682124050, 34996683196066023464195962875]
P3 = [111913032824849252130, 49063192420997854527679793475]
P4 = [110123909838304503990, 18512376609554805482691445335]
P5 = [109146709187032115370, 10506129421757959855129586475]
P6 = [110382143345238886970, 22567063509763234684093270475]
P7 = [110245179394644403100, 20382223547410442956289336075]
P8 = [108522553923729999720, 17018033523451040060797113555]
P9 = [108512500742043656106, 17163334387154750309786061867]
P10 = [109741057847530716000, 13297340647117901361820923075]
P11 = [108902034932485796850, 12260441074498263650721717075]
P12 = [110291739877102075140, 21117334974942773428569817185]
P13 = [111294342929434080810, 38103895579546047175336101675]

Some curves with torsion group Z/3Z and rank = 8, 9, 10, 11 or 12
High rank curves with prescribed torsion Andrej Dujella home page