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arXiv · 1005.4660

The maximum number of rational points for a genus 4 curve over F_7 is 24

Alessandra Rigato
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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 F_7 is 24. It is known that a genus 4 curve over F_7 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 F_7 having 24 points.

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Alessandra Rigato. 2010-05-25. The maximum number of rational points for a genus 4 curve over F_7 is 24. https://arxiv.org/abs/1005.4660

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