Hi John, I am in favour of the current behaviour.
I would define ordinary as "the Tate module T_p(E) contains a 1-dimensional subspace fixed by the local Galois group such that inertia acts trivially on the quotient". So it is ordinary in the sense of Galois representation. This then includes multiplicative reduction, but excludes additive reduction. So the test of p|a_p is valid in all cases. Probably the documentation isn't clear on this. Supersingular reduction is then different from non-ordinary reduction. But I see no reason why not to extend the definition of ordinary in a meaningful way to bad reduction cases. Many things behave the same way for all ordinary cases, e.g. Iwasawa theory. So here is my -1 Chris On 9 October 2017 at 11:19, John Cremona <[email protected]> wrote: > I think that the correct definition for an elliptic curve over Q (or a > number field) to have "ordinary reduction" at a prime p is that it has > good reduction and the reduced curve is ordinary. Similarly for > supersingular. But Sage does not check for good reduction in > E.is_ordinary(p), only that p does not divide E.ap(p), so curves with > bad multiplicative reduction come out as True. On the other hand > E.is_supersingular() tests for good reduction so when p is bad, > E.supersingular(p) will always return False. > > Do people agree? If so we should make a ticket to add the good > reduction test to E.is_ordinary(p). > > John > > -- > You received this message because you are subscribed to the Google Groups > "sage-nt" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send an email to [email protected]. > Visit this group at https://groups.google.com/group/sage-nt. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at https://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/d/optout.
