Rational Points on Elliptic Curves pp 107-144 | Cite as

# Cubic Curves over Finite Fields

Chapter

## Abstract

In this chapter we will look at cubic equations over a finite field, the field of integers modulo with coefficients in F

*p*. We will denote this field by F_{ p }. Of course, now we cannot visualize things; but we can look at polynomial equations$$C:F\left( {x,y} \right) = 0$$

_{ p }and ask for solutions (*x*,*y*) with*x*,*y*∈ F_{ p }. More generally, we can look for solutions*x*,*y*∈ F_{ q }, where F_{ q }is an extension field of F_{ p }, containing*q*=*p*^{ e }elements. We call such a solution a point on the curve*C*. If the coordinates*x*and*y*of the solution lie in F_{ p }, we call it a*rational point*.## Keywords

Modular Form Elliptic Curve Finite Field Elliptic Curf Finite Order
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1992