Download Arithmetic, Geometry, Cryptography and Coding Theory 2009 by David Kohel, Robert Rolland (ed.) PDF

By David Kohel, Robert Rolland (ed.)

ISBN-10: 0821849557

ISBN-13: 9780821849552

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Extra info for Arithmetic, Geometry, Cryptography and Coding Theory 2009

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Of any genus, over any perfect field)? 4. Extremal properties The curve C2 can be found in many places in the existing literature. It enjoys some remarkable properties concerning the number #C2 (F2m ) of F2m -rational points for various values of m. First, it has no F2 -rational points. However, over F4 and F8 it has 14 and 24 points, respectively; in both cases, this is the maximal number of rational points possible on a complete nonsingular genus 3 curve, and in each case C2 is the unique curve obtaining this bound (up to isomorphism).

255–281 (2009) [6] N. Elkies, The Klein quartic in number theory, pp. 51–102 in S. ), The eightfold way: the beauty of Klein’s quartic curve, MSRI Publication Series 35, Cambridge University Press, 352 pp. (1999) [7] A. Enge, How to distinguish hyperelliptic curves in even characteristic, proceedings of Public– key Cryptography and Computational Number Theory (Warsaw 2000), de Gruyter, Berlin, pp. 49–58 (2001) ´ndez Encinas, J. Mun ˜oz Masqu´ [8] J. Espinosa Garc´ıa, L. Herna e, A review on the isomorphism classes of hyperelliptic curves of genus 2 over finite fields admitting a Weierstrass point, Acta Appl.

Cette courbe a un unique point a` l’infini. Ses points singuliers sont les points (0, 0), (0, 1) et le point a` l’infini. La valuation en (0, 0) de x (resp. u) est v(0,0) (x) = 3 (resp. v(0,0) (u) = 7). La valuation en l’infini de x (resp. u) est v∞ (x) = −6 (resp. v∞ (u) = −7). 8). 7 Soit C2 la courbe d’´equation affine (v 4 +v)3 = γx7 . Elle a un unique point a` l’infini. Ses points singuliers sont le point a` l’infini et les points (0, 0), (0, 1), (0, ζ), (0, ζ 2). La valuation en l’infini de x (resp.

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