On the group orders of elliptic curves over finite fields

Details On the group orders of elliptic curves over finite fields On the group orders of elliptic curves over finite fields

2001-10-24

arxiv.org/abs/math/0110262v1

Compositio Math. 85 (1993) 229--247

Mathematics

Number Theory

18 pages, LaTeX. This is a preprint version from 1992

Scientific paper

Given a prime power q, for every pair of positive integers m and n with m dividing the GCD of n and q-1, we construct a modular curve over F_q that parametrizes elliptic curves over F_q along with F_q-defined points P and Q of order m and n, respectively, with P and (n/m)Q having a given Weil pairing. Using these curves, we estimate the number of elliptic curves over F_q that have a given integer N dividing the number of their F_q-defined points.

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