Abstract
We consider the problem of finding an upper bound for the possible torsion of a divisor on a curve of genus 2, when everything is defined over an algebraic number field. Mainly, we show how to write the equation of the Kummer surface of the Jacobian of a curve of genus 2 in terms of the equation of the curve. This allows one to calculate a bound on the torsion which seems better than the bound derived from Riemann-Weil theory. Finally, we discuss briefly a different approach which is valid for all hy — perelliptic curves, at the cost of a considerable increase in complexity.
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