On 8 September 2017 at 09:59, Jeroen Demeyer <jdeme...@cage.ugent.be> wrote: > For completeness: > > We should also consider negatives. But it turns out that going from P to -P > simply turns (a,b,c) in (b,a,c). > > There is also a torsion point T = (56 : 728 : 1) > > Adding that point gives genuinely different solutions. With the torsion > point, the first solution is psi(13*P + T). > > The torsion has order 6, but 2*T simply corresponds to a permutation of the > 3 numbers (a,b,c).
That's a beautiful observation! I had not looked at the torsion. What you are saying is that the obvious symmetries via permutations correspond to negatin the point or adding a point of order 3, but that there is another symmetry of order, adding a point of order 2. What does that look like in terms of (a,b,c)? > > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
