Mestre, Jean-François Construction d’une courbe elliptique de rang \(\geq 12\). (English) Zbl 0541.14027 C. R. Acad. Sci., Paris, Sér. I 295, 643-644 (1982). The author describes a method for constructing elliptic curves E of high rank defined over the rational numbers. The basic idea is that the rank of E is likely to be large if the number \(N_ p\) of points of E modulo p (where p is a prime at which E has good reduction) is as large as possible for all \(p\leq P_ 0,\) where \(P_ 0\) will depend on the computing capacity availabe. Taking \(P_ 0=17\), the author obtains various curves of ranks 6,7,8,9; taking \(P_ 0=37\), he obtains a curve of rank at least 12. Reviewer: I.G.Macdonald Cited in 2 ReviewsCited in 15 Documents MSC: 14H45 Special algebraic curves and curves of low genus 14H52 Elliptic curves 14H25 Arithmetic ground fields for curves 14-04 Software, source code, etc. for problems pertaining to algebraic geometry Keywords:constructing elliptic curves of high rank PDF BibTeX XML Cite \textit{J.-F. Mestre}, C. R. Acad. Sci., Paris, Sér. I 295, 643--644 (1982; Zbl 0541.14027)