Turkish Journal of Mathematics




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 F_5 and F_7. 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 y_1^3 = \frac{5(x + 2)(x + 5)}{x}, y_2^3 = \frac{3x^2(x + 5)}{x + 3} over F_7 has genus 7 with 36 rational points. As this coincides with the Ihara bound, we conclude that the maximum number N_7(7) of F_7-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.

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