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arXiv:math/0110262 [math.NT]AbstractReferencesReviewsResources

On the group orders of elliptic curves over finite fields

Everett W. Howe

Published 2001-10-24Version 1

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.

Comments: 18 pages, LaTeX. This is a preprint version from 1992
Journal: Compositio Math. 85 (1993) 229--247
Categories: math.NT, math.AG
Subjects: 11G20, 14G15, 14H52
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