John Cremona on Thu, 28 May 2020 14:43:15 +0200


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Re: CONSTRUCTING ELLIPTIC CURVES OF PRESCRIBED ORDER


On Thu, 28 May 2020 at 12:41, Michael Hortmann
<michael.hortmann@gmail.com> wrote:
>
> https://openaccess.leidenuniv.nl/bitstream/handle/1887/4425/Thesis.pdf
> https://www.win.tue.nl/diamant/symposium05/abstracts/broeker.pdf
> https://link.springer.com/chapter/10.1007/978-3-540-24847-7_8
>
> No CM.
>
> Other people have worked on the same topic, but I haven't seen a similarly powerful algorithm; it should work for "rather large" :-) numbers. An implementation would really be useful. If I had to do it it would take me at least a month. But somebody may have done it already.
>
> I have written to Peter Stevenhagen, no answer yet.
> Reinier Bröker seems to have disappeared.

Reinier Bröker works at CCR in Princeton.

> So I thought of putting the question on your mailing list.
>
>
> On Thu 28. May 2020 at 13:16, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> wrote:
>>
>> On Thu, May 28, 2020 at 09:21:02AM +0200, Michael Hortmann wrote:
>> > There is an algorithm by Bröker/Stevenhagen for constructing elliptic
>> > curves of prescribed order. Has anybody seen an implementation for Pari/gp?
>> > (Or another computer algebra system)?
>>
>> Could you give a reference to the algorithm ?
>> Is it based on complex-multiplication theory ?
>>
>> Cheers,
>> Bill.
>>