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arXiv · 2102.12977

Two-descent on some genus two curves

Tim Evink·Gert-Jan van der Heiden·Jaap Top
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Abstract

For the hyperelliptic curve C_p with equation y^2=x(x-2p)(x-p)(x+p)(x+2p) with p a prime number, we discuss bounds for the rank of its Jacobian over Q, find many cases having 2-torsion in the associated Shafarevich-Tate group, and we present some results on rational points of C_p.

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Tim Evink, Gert-Jan van der Heiden, Jaap Top. 2021-02-25. Two-descent on some genus two curves. https://arxiv.org/abs/2102.12977

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