Average Normalisations of Elliptic Curves
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Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field Fp 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.
William D. Banks and Igor E. Shparlinski (2002). Average normalisations of elliptic curves. Bulletin of the Australian Mathematical Society, 66, pp 353-358.