Date: Thu, 19 Jan 1995 19:39:35 +1000
To: rusin@math.niu.edu (Dave Rusin)
From: alf@macadam.mpce.mq.edu.au (Alf van der Poorten)
Subject: Re: Question concerning elliptic curves/Q of high rank

At 12:54 on 18/1/95, Dave Rusin wrote concerning "Re: Question concerning
elliptic curves/Q of high rank" that:>In article
<v01510102ab3904afb79a@[137.111.220.192]> you write:
>>I'd like to be able to quote some extreme examples. Is $r=21$ indeed the
>>current record? I'd be grateful for data and/or accessible sources.
>
>I have not kept up with this over the last few years. The best record
>I have is r=17 (Nagao, Japan Acad v. 68 p 289) although I know he and
>J-F Mestre were making progress in this direction a few years ago. Can
>you supply a citation? Are there high-rank examples in infinite families?
>(r=12 is the best I know of in that case).
>
>dave


AU: Nagao,-Koh-ichi
TI: An example of elliptic curve over ${\bf Q}$ with rank $\ge 20$.
PY: 1993
JN: Proc.-Japan-Acad.-Ser.-A-Math.-Sci.
[Japan-Academy.-Proceedings.-Series-A.-Mathematical-Sciences] 69 (1993),
no. 8, 291--293.

I haven't gotten hold of this yet, but a number of correspondents refer to
$21$ rather than $20$.

Alf van der Poorten
ceNTRe for Number Theory Research, School of MPCE
Macquarie University  NSW Australia 2109
alf@mpce.mq.edu.au     http://www.mpce.mq.edu.au/~alf/
fax: +61 2 850 9502
home fax: +61 2 415 6282 [will not work if I'm on line]