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Examples of torsion points on genus two curves. (English) Zbl 1007.11038

Summary: We describe a method that sometimes determines all the torsion points lying on a curve of genus two defined over a number field and embedded in its Jacobian using a Weierstrass point as base point. We then apply this to the examples \(y^{2}=x^{5}+x\), \(y^{2}=x^{5}+5 x^{3}+x\), and \(y^{2}-y=x^{5}\).

MSC:

11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
14G25 Global ground fields in algebraic geometry

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