Torsion group Z/2Z × Z/4Z, rank = 10

Singh (2026)

y2 = x3 + x2 - 417156667767991476045741577332184861400180x 
    + 103463319028436459798460425223784317596906483409448995325761600

	Torsion points:

O, [569870464293245217310, -7127750368935806743183857615270], 
[569870464293245217310, 7127750368935806743183857615270], 
[358121224317819681115, 0], 
[387480259524520325140, 0], 
[205090054755795432970, 5151224983999871384920286867970], 
[205090054755795432970, -5151224983999871384920286867970], 
[-745601483842340006256, 0]

	Independent points of infinite order:

P1 = [145828140360354673135, 6762491906113320449390552536470]
P2 = [304957951194574032178, 2146850750778671846099875646886]
P3 = [-366958824336710045342, 14391956512473637357139777334294]
P4 = [120564594754268738050, 7410904118898808435591414220490]
P5 = [203334674398190451940, 5200747432469972537618323536600]
P6 = [356157090384514806315, 260352418718251806272192325900]
P7 = [-407762824441140436830, 14344523793045553961125544157270]
P8 = [397639191479126812990, 677470139196636223246100559750]
P9 = [75290857298577038095, 8513638362088734891941220826530]
P10 = [224496723803455952980, 4596452389681632117851965068240]
Some curves with torsion group Z/2Z × Z/4Z and rank = 6, 7, 8 or 9
High rank curves with prescribed torsion Andrej Dujella home page