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

On Sunday, November 26, 2023 at 10:16:53 AM UTC-6 John Cremona wrote:

> https://github.com/sagemath/sage/issues/36780
>
> On Saturday, 25 November 2023 at 15:11:53 UTC John Cremona wrote:
>
>> 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
>>
>> On Friday, 24 November 2023 at 03:50:54 UTC hbetx9 wrote:
>>
>>> 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
>>>
>>

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