William Stein on Mon, 11 Jun 2012 16:57:36 +0200

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Re: ell from j

On Mon, Jun 11, 2012 at 7:38 AM, Andreas Enge <andreas.enge@inria.fr> wrote:
> On Fri, Jun 08, 2012 at 09:37:39PM +0200, Bill Allombert wrote:
>> It has been suggested to add a function to PARI which return an elliptic curve with
>> a prescribed j-invariant.
>> An example of such function is
>> ellfromj(j)=if(j==0,[0,0,0,0,1],if(j==1728,[0,0,0,1,0],[0,0,0,3,2]*(j/(1728-j))));
>> How should we call it ? What should it return ? (an ell2,an ell5, a smallell, etc ?)
> How about calling it "ellinit", using just a scalar parameter?

Just a note -- that's what I did with Sage for a while, e.g.,


produced a curve with j-invariant j.  This caused no end of confusion
and bugs in user code, since it is so similar to


where v is a list of invariants or


People were so annoyed by my choice, they deprecated it.

> Andreas

William Stein
Professor of Mathematics
University of Washington