Computing rational points on rank 1 elliptic curves via <IMG ALIGN=BOTTOM HEIGHT=14 WIDTH=12>-series and canonical heights期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Computing rational points on rank 1 elliptic curves via -series and canonical heights

Authors:	Joseph H Silverman

Institution:	Mathematics Department, Box 1917, Brown University, Providence, RI 02912 USA

Abstract:	Let $E/\mathbb{Q}$ be an elliptic curve of rank 1. We describe an algorithm which uses the value of and the theory of canonical heghts to efficiently search for points in $E(\mathbb{Q})$ and $E(\mathbb{Z}_{S})$ . For rank 1 elliptic curves $E/\mathbb{Q}$ of moderately large conductor (say on the order of $10^{7}$ to $10^{10}$ ) and with a generator having moderately large canonical height (say between 13 and 50), our algorithm is the first practical general purpose method for determining if the set $E(\mathbb{Z}_{S})$ contains non-torsion points.

Keywords:	Elliptic curve canonical height

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