Number Theory

Please show all work using only Sage code for both parts. Please do not use already posted responses and code.

Let E be the elliptic curve y$^2=$x$^3+$x$+2$over Z$/13$Z$,$and let P $=(6,4)$ in E$($Z$/13$Z$).$You are eavesdropping on a secret message between Michael and Nikita encrypted using E and P$.$You discovered Michael's secret key is m$=5$and Michael sent Nikita $5$P$=(7,12).$You also know Nikita sent Michael nP$=(6,9).$Use Sage and brute force to find:

$($a$)$Nikita$\text{'}$s secret key n

$($b$)$Michael and Nikita's shared secret key nmP