Translator Disclaimer
2019 Symmetric diophantine systems and families of elliptic curves of high rank
Ajai Choudhry
Rocky Mountain J. Math. 49(5): 1419-1447 (2019). DOI: 10.1216/RMJ-2019-49-5-1419

Abstract

While there has been considerable interest in the problem of finding elliptic curves of high rank over $\mathbb {Q}$, very few parametrized families of elliptic curves of generic rank $\geq 8$ have been published. In this paper we use solutions of certain symmetric diophantine systems to construct a number of families of elliptic curves whose coefficients are given in terms of several arbitrary parameters and whose generic rank ranges from at least 8 to at least 12. Specific numerical values of the parameters yield elliptic curves with quite large coefficients and we could therefore determine the precise rank only in a few cases where the rank of the elliptic curve $\leq 13$. It is, however, expected that the parametrized families of elliptic curves obtained in this paper would yield examples of elliptic curves of much higher rank.

Citation

Download Citation

Ajai Choudhry. "Symmetric diophantine systems and families of elliptic curves of high rank." Rocky Mountain J. Math. 49 (5) 1419 - 1447, 2019. https://doi.org/10.1216/RMJ-2019-49-5-1419

Information

Published: 2019
First available in Project Euclid: 19 September 2019

zbMATH: 07113695
MathSciNet: MR4010569
Digital Object Identifier: 10.1216/RMJ-2019-49-5-1419

Subjects:
Primary: 11G05
Secondary: 11D25, 11D41

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
29 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 5 • 2019
Back to Top