This issue is #20391 on trac, and was supposed to have been resolved by 
#18916 (which is fixed in sage 7.4). But it looks like it's not, even 
though the similar test case:

sage: x = polygen(GF(4099))
sage: H = HyperellipticCurve(x^6 + x + 1)
sage: H.count_points(1)


that I had been using does now work.


Kiran


On Sunday, October 9, 2016 at 10:06:06 AM UTC-7, John Cremona wrote:
>
> I have not before now used Sage to count points on hyperelliptic 
> curves over finite fields, only elliptic curves.  Am I doing something 
> wrong or is this a bug?  It certainly looks like a bug. 
>
> sage: F=GF(23) 
> sage: x=polygen(F) 
> sage: C=HyperellipticCurve(x^8+1) 
> sage: C.cardinality() 
> ... 
> ValueError: Q must be a monic polynomial of odd degree >= 3 
>
> According to C.count_points_exhaustive() the answer is 24. 
>
> John Cremona 
>

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