I am trying to work out an example problem in which I have to find order of $P(1/2,1/2)$ on the elliptic curve $ y^2 = x^3 + x/4 $ .
So Far I have done the following:
1) Given equation of the curve, found out the equation of tangent at P (it is $y = x$). Then found the intersection with the curve at $(0,0)$. Verified this by using the formula for finding $2P$. So $2P$ is $(0,0)$
Now my problem is given $P$ and $2P$ how do I proceed further to find $3P$ and so on.
I have used the $P+Q$ result here to find $3P$ as $(1/2,0)$ but I cannot seem to obtain it using the geometrical interpretation.
Any explanation to proceed with this will be really helpful.