The rank of elliptic curves with rational 2-torsion points over large fields

Author:
Bo-Hae Im

Journal:
Proc. Amer. Math. Soc. **134** (2006), 1623-1630

MSC (2000):
Primary 11G05

Published electronically:
December 15, 2005

MathSciNet review:
2204272

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Abstract: Let be a number field, an algebraic closure of , the absolute Galois group , the maximal abelian extension of and an elliptic curve defined over . In this paper, we prove that if all 2-torsion points of are -rational, then for each , has infinite rank, and hence has infinite rank.

**1.**B. Im: Mordell-Weil groups and the rank over large fields of elliptic curves over large fields, arXiv: math.NT/0411533, to appear in*Canadian J. Math.***2.**B. Im: Heegner points and Mordell-Weil groups of elliptic curves over large fields, arXiv: math.NT/0411534,*submitted for publication*, 2003.**3.**Serge Lang,*Fundamentals of Diophantine geometry*, Springer-Verlag, New York, 1983. MR**715605****4.**Michael Larsen,*Rank of elliptic curves over almost separably closed fields*, Bull. London Math. Soc.**35**(2003), no. 6, 817–820. MR**2000029**, 10.1112/S0024609303002431**5.**Joseph H. Silverman,*Integer points on curves of genus 1*, J. London Math. Soc. (2)**28**(1983), no. 1, 1–7. MR**703458**, 10.1112/jlms/s2-28.1.1

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Additional Information

**Bo-Hae Im**

Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112

Email:
im@math.utah.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08494-7

Received by editor(s):
January 28, 2005

Published electronically:
December 15, 2005

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2005
American Mathematical Society