Rank ≥ 27

Elkies (2016)

y2 + xy = x3 - 55671146865244401916117773020296610079754015500970x  
              + 161981895322788558220906653027519611838007321625214218991719656790551905956 

	Independent points of infinite order: 

P1 = [3767967516008165080365044, 2389736302094908158004099904947501190]
P2 = [6870254134405565034404108, 10187524517965617942800545361683736678]
P3 = [3887185284020449623939380, 2077020998301366905747533719381033926]
P4 = [4704247833799635063001076, 2048360739972031724784820678863578246]
P5 = [4126561570009022393013236, 1587663907962563318996362180056025478]
P6 = [4589477829219012602846900, 1774818405716699582839388275297252934]
P7 = [1744288391661626065189796, 8377495495389391047035879698795823126]
P8 = [375965292932773063399988, 11878746522289663117790823052090948358]
P9 = [-4430058725939313297140384, 17935065674772418581237173320631279206]
P10 = [46029381695079838296565796, 308418721198583803941973238472690797126]
P11 = [5015368619774521542769364, 2987769291318668561101046595511063430]
P12 = [55141979583089031946559900, 405905110011451276640435700460385551166]
P13 = [2703830808220294466353748, 5587793124284970779400186615144247334]
P14 = [3412724629872318338319668, 3426156011058008602456511184805561094]
P15 = [272723117214107051072886140, 4502171870151657762741942725666306991014]
P16 = [4732850534022088572670964, 2124602225002897987491873188898646406]
P17 = [19225480790209113087907256, 78725996092378368618479740248297817478]
P18 = [5213267756598937117846508, 3666105463387143768198032469471386414]
P19 = [-4503215618194252049902522, 17926532987110694852440283715314002874]
P20 = [10358928712485769814651816, 26398450763063898266637186797421380678]
P21 = [6560446866541184312028656, 8894515448962144734398280820434671978]
P22 = [4667249764662401626929236, 1954092716090144351072720616414325286]
P23 = [3131745787384349113625300, 4283649283716227803355987840842617734]
P24 = [243907731994687263474127628, 3807478665185691587984635270031859346574]
P25 = [110171466072672245507182388, 1153803508275547153736593941741941166854]
P26 = [2631452133741740392491152, 5805818938673165314161211507146370634]
P27 = [2398961346477899287733092916, 117498623151243646059583140149253976390406]