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]
High rank curves with prescribed torsion | Andrej Dujella home page |