Re: Question: trying to locate other Diophantine triples from certain elliptic curves

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Tue, Jul 09, 2024 at 07:46:39PM -0700, American Citizen wrote:
> I appreciate all your effort, Bill and John
> 
> Somehow, someway, something got sideways.
> 
> The Diophantine condition is that (a*b+1), (a*c+1) and (b*c+1) are squares. 
> I don't understand how this got changed to (a*b), (a*c) and (b*c) squares.
> 
> Can we start over again, with this understanding?

We understood your question as:
Given a,b,c, find A,B,C so that
E_triple(a,b,c) and E_triple(A,B,C) are isomorphic.
I think we addressed that.

Cheers,
Bill.