How to find the embedding degree of an elliptic curve?

I want to know if there's any algorithm to find the embedding degree of elliptic curve? for example SECP256K1 curve has embedding degree 19298681539552699237261830834781317975472927379845817397100860523586360249056. this number is so large that it can't be found using brute force. So there has to be an algorithm to figure out the embedding degree in acceptable time frame.

First count the number of points on your curve, call this $\ell$. You wish to find the smallest $k$ such that $\ell$ divides $p^k-1$. Equivalently, the smallest $k$ such that $p^k\equiv 1\pmod\ell$. For prime $\ell$ this tells us that $k|(\ell-1)$ by Fermat’s little theorem. For $\ell$ of size 256 bits, factoring $\ell -1$ is not too hard and the number of factors is amenable to exhaustion (though there are cleverer ideas than naive exhaustion).