Abstract
In his famous article [N1], N6ron has given a method for constructing an infinite family of elliptic curves over Q with rank at least 11. By studying this from the viewpoint of Mordell-Weil lattices IS 1, S 2, S 3], we find that N6ron's method gives a complete algorithm for such a construction. In particular, we can write down an explicit numerical example. N6ron's idea is a very ingeneous, beautiful combination of some deep results in algebraic geometry and number theory. The former is based on the theory of del Pezzo surfaces (cf. [M, DP]) and the latter is the specialization argument originated by N6ron, which has been strengthened by Silverman and Tate (cf. [Sil , T]). Another ingredient implicit in IN1] seems to be the idea leading to the Kodaira-N6ron model (an elliptic surface) of an elliptic curve over a function field, which was to be developed later in [N2]. Our contribution, if any, will be:
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
