Sequences of Jacobian Varieties with Torsion Divisors of Quadratic Order

Abstract

A fortuitous intersection of work on periodic continued fraction expansions in hyperelliptic function fields and the study of parametrized families of quadratic number fields with high class number leads us to discover sequences of hyperelliptic curves whose Jacobians contain torsion divisors of order $g^2$. These sequences generalize those earlier constructed by Flynn and by Leprévost.