$(1$ point$)$ Consider the elliptic curve group based $on$ the equation

$y^2-=x^3+ax+b,$modp

where $a=1,b=6,$ and $p=7.$

This curve contains the point $P=(1,1).$ The order $of$ this elliptic curve group $is$ the prime number $11,$ and

therefore $we$ can $be$ sure that $Pis$ a primitive element. Another element $in$ this group $isQ=(4,2).$ The index $ofQ$

with respect $toPis$ the least positive integer $d$ such that $Q=dP.$ What $isd,$ the index $ofQ?$