Finding an x such that xP = (11,44) on an elliptic curve Given the elliptic curve

$$E:y^2 = x^3+17x+5 \mod 59$$

with point $P = (4,14)$, how do I find $x$ such that compute $x\cdot P = (11,44)$

Is there a mathematical method to compute $x$, or do I simply compute a lot  of $x$'s and hope for the best?

If it helps, I know $8P = (16,40)$
As mentioned by Thekwasti, what you want here is compute a discrete logarithm, but while it is true that in general computing discrete logarithms is "hard" (which is why they are used in cryptography), in your case the group is small enough to make even a brute force search completely feasible. So the goal of the exercise is probably to make you implement at least one of the following algorithms:


Brute force search
Shanks's "baby step, giant step"
Pollard's rho


You will normally find that they are in increasing order of efficiency (although here the group is so small that the difference might not be noticeable).