Rank = 10

Elkies and Watkins (2004)

y2 + y = x3 - 16312387x + 25970162646

Independent points of infinite order: 

P1 = [2654, -37029]
P2 = [-4476, 96486]
P3 = [-4523, 84980]
P4 = [-4617, 53528]
P5 = [-4628, 48369]
P6 = [-4654, 32919]
P7 = [-4672, 14253]
P8 = [-4674, 10235]
P9 = [-18111/4, 669675/8]
P10 = [-18663/4, 180649/8]