Torsion Points of Elliptic Curves
نویسنده
چکیده
Elliptic curves as an area of mathematical study are initially simple to understand, but reveal startling complexity when considered over different fields. This paper discusses the general properties and characteristics of projective space, elliptic curves, and the group structure that arises with certain binary operations on the curve. We discuss elliptic curves over Q, including the topic of the discriminant and a proof of the Nagell-Lutz theorem. Finally, we discuss the properties of elliptic curves over finite fields, including a proof of the Reduction Modulo p Theorem.
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