Two-descent on some genus two curves
Number Theory
2021-02-26 v1
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.
Cite
@article{arxiv.2102.12977,
title = {Two-descent on some genus two curves},
author = {Tim Evink and Gert-Jan van der Heiden and Jaap Top},
journal= {arXiv preprint arXiv:2102.12977},
year = {2021}
}
Comments
17 pages