The maximum number of rational points for a genus 4 curve over F7 is 24
Abstract
In this paper we show that the maximum number of rational points possible for a smooth, projective, absolutely irreducible genus 4 curve over a finite field F7 is 24. It is known that a genus 4 curve over F7 can have at most 25 points. In this paper we prove that such a curve can have at most 24. On the other hand we provide an explicit example of a genus 4 curve over F7 having 24 points.
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