Constructing elliptic curves over finite fields with prescribed torsion

Details Constructing elliptic curves over finite fields with prescribed torsion Constructing elliptic curves over finite fields with prescribed torsion

2008-11-03

arxiv.org/abs/0811.0296v4

Math. Comp. 81 (2012), 1131-1147

Mathematics

Number Theory

Corrected typos in the statement of Lemma 2, 17 pages

Scientific paper

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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