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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