Torsion group Z/6Z, rank = 9


Klagsbrun (2020)

y2 + xy = x3 - 801598222309406030167646512525x 
	    + 1340218010187071010144873439749301626926500625

	Torsion points: 

O, [-1341797659453694, 670898829726847], 
[40442310512450, -36164425532426234145025], 
[40442310512450, 36164425491983923632575], 
[1985891276172650, 87064446031542861779975], 
[1985891276172650, -87064448017434137952625]

	Independent points of infinite order:

P1 = [790071801566192, 34642044937854378014327]
P2 = [-726457590523390, -39232179492604220813185]
P3 = [-1339807100575790, -3023236219045337181425]
P4 = [625652233410050, 32918110979399066318975]
P5 = [209151625439330, 34376032998628737907295]
P6 = [989978630755400, 38947259601397055558375]
P7 = [1119915446189750, 42977966010216237307475]
P8 = [3840854243430050, 234355065188019636758975]
P9 = [3153193539638450, 173676878795099877156575]

Voznyy (2020)

y2 + xy = x3 - 131191625735555376835902425161835407770610x 
	    + 9527282740506020999783481471335892905756009749531992669364100

	Torsion points: 

O, [601056961771264820, -3073829747672592479720757761410], 
[-394160735743214223484, 197080367871607111742], 
[454189933592245618820, -6605719125152184954068158313410], 
[454189933592245618820, 6605719124697995020475912694590], 
[601056961771264820, 3073829747671991422758986496590]

	Independent points of infinite order:

P1 = [61211304441831519620, 1313856981979888966235357065790]
P2 = [72281378181638789320, 649778688229362276157348444090]
P3 = [-352880613877821574780, -3446723346615340585312024975810]
P4 = [420294701930403826820, 5350906766255423009742764406590]
P5 = [15898354312641568820, 2728657219706761181086299744590]
P6 = [1032983459250642436820, 31245135458563749975261525516590]
P7 = [-58698985974962247340, -4126238798011380247851183861250]
P8 = [18022027324314945409460, 2418900981656785462501766758989950]
P9 = [12478365919747619890820, 1393331990648175340750274739606590]

Dujella - Peral (2026)

y2 + xy = x3 + 42459070568638227676679977396779231730x 
	    + 119881395284563761312108211303985196714695782262476368900

	Torsion points: 

O, [-2468983906018901060, 1234491953009450530], 
[1053899286348729340, 12876317380569789385029180130], 
[1053899286348729340, -12876317381623688671377909470], 
[14774481697605930820, -63025744472413493072333241470], 
[14774481697605930820, 63025744457639011374727310650]

	Independent points of infinite order:

P1 = [-31033395220068260, -10888696720875752056116741470]
P2 = [-1232864448860804240, -8103161016824343141105844670]
P3 = [-1328315624621856260, -7819120064970281438189301470]
P4 = [3802553855770780126, 18338947764785709323657418652]
P5 = [-2433590726687000900, -1463142233956860582883774430]
P6 = [3867651990684847612, 18491984028573822481136771362]
P7 = [-1218313370645706530, -8145220354674240158153680250]
P8 = [-1878910201911913560, -5785455130632454988224496970]
P9 = [28632932208035602735/4, 224941354774375071659805792365/8]

Some curves with torsion group Z/6Z and rank = 6, 7 or 8
High rank curves with prescribed torsion Andrej Dujella home page