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      Constructing elliptic curves over finite fields with prescribed torsion

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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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          Most cited references13

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          Bornes pour la torsion des courbes elliptiques sur les corps de nombres

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            A tameness criterion for Galois representations associated to modular forms $(\mod p)$

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              Universal Bounds on the Torsion of Elliptic Curves

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                Author and article information

                Journal
                10.1090/S0025-5718-2011-02538-X
                0811.0296
                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Number theory
                Number theory

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