On Sun, Dec 27, 2015 at 12:05 PM, Andrey Novoseltsev <novos...@gmail.com> wrote: > A report from Lee Morgenstern using SageMathCell running Sage 6.9.beta6, but > the same happens in 6.10: > > the following code produces > NTLError: RR: division by zero
This curve has a very large conductor and coefficients, at least relative to what mwrank is designed to handle. For example, I get the error ValueError: Invalid input ([0, 4547218754, 0, 1581862737670677504, 0]) to mwrank (singular curve) when calling E.mwrank(), which suggests long int overflow. I've cc'd John Cremona. John: what should Sage be checking before allowing E.mwrank to create a curve using mwrank? In this case, very likely E.rank() should instantly raise a NotImplementedError. To the original person asking the question, you might try using Simon Spicer's new function: E.analytic_rank_upper_bound() which gives an upper bound of 1 in a few seconds; as the root number is -1, the rank of this curve *must* be 1 (by Gross-Zagier-Kolyvagin). This is, of course, exactly the hardest case for computing the MW-group explicitly using mwrank. Using Heegner points or higher descents (as in Magma) is probably the only hope here... In any case, E.rank() is definitely 1. See https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/2015-12-27-rank-divzero.sagews for a worksheet illustrating the above. > > > m = 239; n = 48 > X = 2*m*n; Y = m^2 - n^2; Z = m^2 + n^2 > E = EllipticCurve([0, 2*(Z^2-X*Y), 0, (X*Y)^2, 0]) > E.rank() > > > The same error also happens with E.gens(), > but takes longer to get it. But if you use > E.gens(descent_second_limit=9) > you can get the error sooner. > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- William (http://wstein.org) -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
