Possible error: isogeny classes

[hbetx9]

Hi,

 

 In some work on isogeny clases, my team ran across the following of two elliptic curves which are isogenous but sage reports different isogeny classes for them. Is there some  technicalities (j = 0) leading to incorrect output or is this something that we should flag a bug?

sage: L5.<r5> = NumberField(x^2-5)

sage: E = EllipticCurve(L5,[287275052073119826051072\*r5-642366544675288047943680,-125329261653845158603060848774610944\*r5+280244748627855491701953075326484480])

sage: F = EllipticCurve(L5,[0,-4325477943600\*r5-4195572876000])

sage: E.isogeny_class().matrix()
[ 1 25 75  3  5 15]
[25  1  3 75  5 15]
[75  3  1 25 15  5]
[ 3 75 25  1 15  5]
[ 5  5 15 15  1  3]
[15 15  5  5  3  1]

sage: F.isogeny_class().matrix()
[1 3]
[3 1]

sage: E.is_isogenous(F)
True

Best,

Lance

[John Cremona]

Thanks for this report, which certainly indicates a bug.  I will look into it as the code here was written by me.  I note that the two curves have CM (by the order of index 5 and the maximal order in Q(sqrt(-3)) respectively), and the code to deal with isogenies is different in this case. The relevant function is isogeny_degrees_cm(), imported from sage.schemes.elliptic_curves.isogeny_class.  And for some reason that function is not including the valid isogeny prime 5.

If you do F.isogeny_class(reducible_primes=[3,5]) you get the same as for E (but you have to so that in a fresh Sage session becauses of caching of previously computed results).

John Cremona

[John Cremona]

https://github.com/sagemath/sage/issues/36780

[hbetx9]

Hi John,

 Thanks a bunch for the pointed reply. Glad to hear we weren't missing something easy and thanks a bunch for filling the bug report!

Best,
Lance