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arXiv · 2008.05253

On the number of point of given order on odd degree hyperelliptic curves

John Boxall
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Abstract

For integers $N\geq 3$ and $g\geq 1$, we study bounds on the cardinality of the set of points of order dividing $N$ lying on a hyperelliptic curve of genus $g$ embedded in its jacobian using a Weierstrass point as base point. This leads us to revisit division polynomials introduced by Cantor in 1995 and strengthen a divisibility result proved by him. Several examples are discussed.

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John Boxall. 2020-08-12. On the number of point of given order on odd degree hyperelliptic curves. https://arxiv.org/abs/2008.05253

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