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Final exercise Elliptic Curves

Deadline: December 21, 2011, at noon.

Exercise: Pick your favorite integer N > 1, and explain why this is your favorite integer. Now construct a prime p and an elliptic curve E/Fpsuch that #E(Fp) = N .

Your code should end with a verification that the curve has the right number of points by using a standard Sage function which counts the number of points of your elliptic curve.

Grading: The grade is based on the size of N (bigger is better) and on the sophistication of your algorithm (write down comments and explain your tricks).

How to hand in: Share your Sage sheet with mkosters and rene.

Remarks: You are allowed to use any function in Sage as long as it doesn’t trivially solve the problem.

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