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

Gordon, Daniel M.; Grant, David

doi:10.1090/S0002-9947-1993-1094558-0

Computing the Mordell-Weil rank of Jacobians of curves of genus two
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by Daniel M. Gordon and David Grant PDF

Trans. Amer. Math. Soc. 337 (1993), 807-824 Request permission

Abstract:

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.

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