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arXiv · 0811.0296

Constructing elliptic curves over finite fields with prescribed torsion

Andrew V. Sutherland
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Abstract

We present a method for constructing optimized equations for the modular curve X_1(N) using a local search algorithm on a suitably defined graph of birationally equivalent plane curves. We then apply these equations over a finite field F_q to efficiently generate elliptic curves with nontrivial N-torsion by searching for affine points on X_1(N)(F_q), and we give a fast method for generating curves with (or without) a point of order 4N using X_1(2N).

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Andrew V. Sutherland. 2008-11-03. Constructing elliptic curves over finite fields with prescribed torsion. https://doi.org/10.1090/s0025-5718-2011-02538-x

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