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ON POSITIVE PROPORTION OF RANK-ZERO TWISTS OF ELLIPTIC CURVES OVER $\mathbb{Q}$

Part of: Arithmetic algebraic geometry Curves

Published online by Cambridge University Press:  07 November 2014

MAOSHENG XIONG
MAOSHENG XIONG*
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong email mamsxiong@ust.hk
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Abstract

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Extending the idea of Dabrowski [‘On the proportion of rank 0 twists of elliptic curves’, C. R. Acad. Sci. Paris, Ser. I 346 (2008), 483–486] and using the 2-descent method, we provide three general families of elliptic curves over $\mathbb{Q}$ such that a positive proportion of prime-twists of such elliptic curves have rank zero simultaneously.

Keywords

elliptic curves2-descentSelmer grouprank

MSC classification

Primary: 11G05: Elliptic curves over global fields
Secondary: 14H52: Elliptic curves
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 98 , Issue 2 , April 2015 , pp. 281 - 288
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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