An exhaustive computer search for finding new curves with many points among fibre products of two Kummer covers over F5 and F7

Authors : - Ferruhözbudak, Burcu Gülmez Temür, Oğuz Yayla

Pages : 908-913

Doi:10.3906/mat-1206-26

View : 12 | Download : 9

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :In this paper we make an exhaustive computer search for finding new curves with many points among fibre products of 2 Kummer covers of the projective line over F5 and F7. At the end of the search, we have 12 records and 6 new entries for the current Table of Curves with Many Points. In particular, we observe that the fibre product y13 = \frac{5(x + 2)(x + 5)}{x}, y23 = \frac{3x2(x + 5)}{x + 3} over F7 has genus 7 with 36 rational points. As this coincides with the Ihara bound, we conclude that the maximum number N7(7) of F7-rational points among all curves of genus 7 is 36. Our exhaustive search has been possible because of the methods given in the recent work by Özbudak and Temür (2012) for determining the number of rational points of such curves.
Keywords : Curves with many points over finite fields, Kummer covers, fibre products