Constructing Elliptic Curves with Prescribed Torsion over Finite Fields
نویسنده
چکیده
The modular curve X1(N) parametrizes elliptic curves with a point of order N . For N ≤ 50 we obtain plane models for X1(N) that have been optimized for fast computation, and provide explicit birational maps to transform a point on our model of X1(N) to an elliptic curve. Over a finite field Fq, these allow us to quickly construct elliptic curves containing a point of order N , and can accelerate the search for an elliptic curve of order divisible by N . For odd N we also give a method to generate elliptic curves over Fq with order congruent to 2N mod 4N .
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