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.
