Examples of genus 2 curves over Q with Jacobians of high Mordell-Weil rank, by Roland B. Dreier

This paper has appeared in International Math Research Notices, 1997, no. 18, pp. 875-880, and so the dvi version has been removed. An example is given of a curve C of genus 2 defined over Q such that its Jacobian J is simple and such that the Mordell-Weil group J(Q) has rank at least 25. An example is also given of a curve C' of genus 2 defined over Q such that its Jacobian is simple and has Mordell-Weil rank at least 19, with the additional property that one of the divisors generating this rank 19 group is supported on C'(Q(sqrt{29})) \ C'(Q).

Roland B. Dreier <dreier@math.berkeley.edu>