Re: Complex AGM

Andreas Enge on Wed, 15 Feb 2012 16:54:27 +0100

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Re: Complex AGM

To: John Cremona <john.cremona@gmail.com>
Subject: Re: Complex AGM
From: Andreas Enge <andreas.enge@inria.fr>
Date: Wed, 15 Feb 2012 16:54:09 +0100
Cc: pari-dev@pari.math.u-bordeaux.fr
Delivery-date: Wed, 15 Feb 2012 16:54:27 +0100
In-reply-to: <CAD0p0K7m1QPJyZHBdQU1-oCyicGmonnFEKKytiCwMsLvskuWbg@mail.gmail.com>
References: <20120215150953.GA11263@yellowpig> <CAD0p0K7m1QPJyZHBdQU1-oCyicGmonnFEKKytiCwMsLvskuWbg@mail.gmail.com>
User-agent: Mutt/1.5.21 (2010-09-15)

On Wed, Feb 15, 2012 at 03:24:21PM +0000, John Cremona wrote:
> For a definition of what "optimal" means and why it matters for
> elliptic curve period computations, see http://arxiv.org/abs/1011.0914

In his PhD thesis, Dupont makes the additional assumption that if there
are two "good" choices, then Im (b_n, a_n) > 0 (it could be that this is
taken from Cox1984, I have not verified). So I would suggest to modify
pari to compute the optimal sequence together with this normalisation.

Andreas

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References:
- Complex AGM
  - From: Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>
- Re: Complex AGM
  - From: John Cremona <john.cremona@gmail.com>

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