The study of elliptic curves is an important part of the elds of
algebraic geometry and number theory, with many applications in areas
such as cryptography. While much of the groundwork has already
been laid out, the results often times fall short of giving an easily digestible
overview of the subject as a whole. The aim of this paper is
to condense a number of high-level results into a much more readily
accessible version that is better suited for a reader encountering elliptic
curves for the rst time. Additionally, the paper provides a toolkit
for identifying elliptic curve groups, detailing steps to take in order to
determine the group behind a given elliptic curve.
2016. , 27 p.