On the group orders of elliptic curves over finite fields

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dc.creatorHowe, Everett W.
dc.date2001-10-24
dc.date.accessioned2026-07-07T04:44:03Z
dc.date.available2026-07-07T04:44:03Z
dc.descriptionGiven 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.
dc.description18 pages, LaTeX. This is a preprint version from 1992
dc.identifierhttps://arxiv.org/abs/math/0110262
dc.identifierhttp://arxiv.org/abs/math/0110262
dc.identifierCompositio Math. 85 (1993) 229--247
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62478
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11G20 (Primary) 14G15, 14H52 (Secondary)
dc.titleOn the group orders of elliptic curves over finite fields
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