# Elliptic Curves

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Let E be the elliptic curve over F5 defined by y^2 = x^3+1.

1. Write down the division polynomial (psi_3)(x) for this curve.

2. Show that the greatest common divisor of (psi_3)(x) and "x^5 -x" is "x(x-1)."

3. Use part (2) to show that the 3-torsion points in E(F5) are {Origin,(0,1),(0,-1)}."

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##### Solution Summary

In this solution we solve several number theory problems involving points on an elliptic curve over a finite field. Included is one reference.

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** Please see the attached file for the complete solution **

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We are given the elliptic curve E over (please see the attached file) defined by:

(please see the attached file)

a) We wish to compute the division polynomial (please see the attached file) for E.

In general, for the elliptic curve defined by (please see the attached file) we have [1]

(please see the attached ...

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