The Geometry of Elliptic Curves over Finite Fields
نویسنده
چکیده
We first provide an overview of the basic results in the geometry of elliptic curves, introducing the Picard Group, Weierstrass Equations, and Isogenies. This is followed by a discussion of the structure of m-torsion points on an elliptic curve, introducing such tools as the Weil pairing and the l-adic Tate module. The paper culminates in a theorem counting the rational points on an elliptic curve over a finite field using the trace of Frobenius.
منابع مشابه
Elliptic Curves over Finite Fields
In this chapter, we study elliptic curves defined over finite fields. Our discussion will include the Weil conjectures for elliptic curves, criteria for supersingularity and a description of the possible groups arising as E(Fq). We shall use basic algebraic geometry of elliptic curves. Specifically, we shall need the notion and properties of isogenies of elliptic curves and of the Weil pairing....
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