Computing the Mordell-Weil Rank of Jacobians of Curves of Genus Two
Daniel M. Gordon, David M. Grant · Transactions of the American Mathematical Society · 1993
We derive the equations necessary to perform a two-descent on the Jacobians of curves of genus two with rational Weierstrass points. We compute the Mordell-Weil rank of the Jacobian of some genus two curves defined over the rationals, and discuss the practicality of using this method.