Trivial torsion group, rank ≥ 28


Elkies (2006)

y2 + xy + y = x3 - x2 - 20067762415575526585033208209338542750930230312178956502x  
              + 34481611795030556467032985690390720374855944359319180361266008296291939448732243429 

	Independent points of infinite order: 

P1 = [-2124150091254381073292137463, 259854492051899599030515511070780628911531] 
P2 = [2334509866034701756884754537, 18872004195494469180868316552803627931531]
P3 = [-1671736054062369063879038663, 251709377261144287808506947241319126049131]
P4 = [2139130260139156666492982137, 36639509171439729202421459692941297527531]
P5 = [1534706764467120723885477337, 85429585346017694289021032862781072799531]
P6 = [-2731079487875677033341575063, 262521815484332191641284072623902143387531]
P7 = [2775726266844571649705458537, 12845755474014060248869487699082640369931]
P8 = [1494385729327188957541833817, 88486605527733405986116494514049233411451]
P9 = [1868438228620887358509065257, 59237403214437708712725140393059358589131]
P10 = [2008945108825743774866542537, 47690677880125552882151750781541424711531]
P11 = [2348360540918025169651632937, 17492930006200557857340332476448804363531]
P12 = [-1472084007090481174470008663, 246643450653503714199947441549759798469131] 
P13 = [2924128607708061213363288937, 28350264431488878501488356474767375899531] 
P14 = [5374993891066061893293934537, 286188908427263386451175031916479893731531]
P15 = [1709690768233354523334008557, 71898834974686089466159700529215980921631]
P16 = [2450954011353593144072595187, 4445228173532634357049262550610714736531]
P17 = [2969254709273559167464674937, 32766893075366270801333682543160469687531] 
P18 = [2711914934941692601332882937, 2068436612778381698650413981506590613531] 
P19 = [20078586077996854528778328937, 2779608541137806604656051725624624030091531]
P20 = [2158082450240734774317810697, 34994373401964026809969662241800901254731]
P21 = [2004645458247059022403224937, 48049329780704645522439866999888475467531]
P22 = [2975749450947996264947091337, 33398989826075322320208934410104857869131]
P23 = [-2102490467686285150147347863, 259576391459875789571677393171687203227531]
P24 = [311583179915063034902194537, 168104385229980603540109472915660153473931]
P25 = [2773931008341865231443771817, 12632162834649921002414116273769275813451] 
P26 = [2156581188143768409363461387, 35125092964022908897004150516375178087331] 
P27 = [3866330499872412508815659137, 121197755655944226293036926715025847322531] 
P28 = [2230868289773576023778678737, 28558760030597485663387020600768640028531] 

An example with rank ≥ 27
Previous record with rank ≥ 24
High rank curves with prescribed torsion Andrej Dujella home page