| 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. >>