GENERATORS AND INTEGRAL POINTS ON CERTAIN QUARTIC CURVES

被引：0
|
作者：
Fujita, Yasutsugu [1 ]
Nara, Tadahisa [2 ]
机构：
[1] Nihon Univ, Coll Ind Technol, 2-11-1 Shin Ei, Narashino, Chiba 2758576, Japan
[2] Tohoku Gakuin Univ, Fac Engn, 1-13-1 Chuo, Tagajo, Miyagi 9858537, Japan
来源：
GLASNIK MATEMATICKI | 2019年 / 54卷 / 02期
关键词：
quartic curve; canonical height; integral points; Y(2);
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study integral points and generators on quartic curves of the forms 442 +4,4 = ra for a nonzero integer ra. 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.
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页码：321 / 343
页数：23
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