Two-descent on some genus two curves

2021/02/25 by Evink, Tim, van der Heiden, Gert-Jan, Top, Jaap
#11G30 #14H25 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2102.12977

Abstract

For the hyperelliptic curve C_p with equation y²=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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