%0 Journal Article
%T Generators and integral points on certain quartic curves
%A Fujita
%A Yasutsugu
%A Nara
%A Tadahisa
%J -
%D 2019
%R 10.3336/gm.54.2.04
%X Sa£żetak In this paper, we study integral points and generators on quartic curves of the forms \(u^2 \pm v^4=m\) for a nonzero integer $m$. The main results assert that certain integral points on the curves can be extended to bases for the Mordell-Weil groups of the elliptic curves attached to the quartic curves in the cases where the Mordell-Weil ranks are at most two. As corollaries, we explicitly describe the integral points on the quartic curves in each case where the ranks are one and two
%K Elliptic curve
%K quartic curve
%K canonical height
%K integral points
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=333805