Michael Hortmann on Thu, 28 May 2020 13:41:20 +0200


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Re: CONSTRUCTING ELLIPTIC CURVES OF PRESCRIBED ORDER

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.
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.