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# 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} }

- Published 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