Average normalisations of elliptic curves

William D. Banks*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field double-struck F signp is isomorphic to a curve y2 = x3 + ax + b with a and b of size O(p3/4). In this paper, we show that almost all elliptic curves satisfy the stronger bound O(p2/3). The problem is motivated by cryptographic considerations.

Original languageEnglish
Pages (from-to)353-358
Number of pages6
JournalBulletin of the Australian Mathematical Society
Issue number3
Publication statusPublished - Dec 2002


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