# Elliptic Curves

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)}."

I have also attached the problem for easier reading.

© BrainMass Inc. brainmass.com October 10, 2019, 5:37 am ad1c9bdddfhttps://brainmass.com/math/curves/elliptic-curves-over-finite-field-511538

#### Solution Preview

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

Thank you for using BrainMass.com. I hope that this helps.

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 ...

#### 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.