Examples of torsion points on genus two curves

Abstract

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}+x , y 2 = x 5 + 5 x 3 + x y^{2}=x^{5}+5\,x^{3}+x , and y 2 − y = x 5 y^{2}-y=x^{5} .