Constructing elliptic curves over finite fields with prescribed torsion
Number Theory
2016-02-24 v4
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).
Keywords
Cite
@article{arxiv.0811.0296,
title = {Constructing elliptic curves over finite fields with prescribed torsion},
author = {Andrew V. Sutherland},
journal= {arXiv preprint arXiv:0811.0296},
year = {2016}
}
Comments
Corrected typos in the statement of Lemma 2, 17 pages