Computing the Mordell-Weil rank of Jacobians of curves of genus two

@inproceedings{Gordon1992ComputingTM,
  title={Computing the Mordell-Weil rank of Jacobians of curves of genus two},
  author={Daniel M. Gordon},
  year={1992}
}
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. Introduction Let C he a curve of genus two defined over a number field K, and J its Jacobian variety. The Mordell-Weil theorem states that J(K) is a finitelygenerated Abelian group, but except in a few special… CONTINUE READING