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Construction d’une courbe elliptique de rang $$\geq 12$$. (English) Zbl 0541.14027
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

##### 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