On Thursday, 17 October 2013 11:12:42 UTC+1, Georgi Guninski wrote: > > E=EllipticCurve(QQ,[-100,0]) > sha=E.sha() > sha.an_padic(13) > > > padic_prec = max(bounds[1:]) + 5 > ValueError: max() arg is an empty sequence
Oooops. That is clearly a bug in something I have written. I will fix this, but I won't be able to do so before the end of the month I fear. You can still get the result in two ways. Either : sage: E = EllipticCurve([-100,0]) sage: sha = E.sha() sage: sha.an_padic(13,use_twists=False) 1 + O(13^2) or redoing what the function actually does : sage: E = EllipticCurve([-100,0]) sage: l = E.padic_lseries(13) sage: f = l.series(3) sage: f 9 + 8*13 + 7*13^2 + 5*13^3 + 8*13^4 + O(13^5) + (12 + O(13^2))*T + (5 + O(13^2))*T^2 + (2 + 8*13 + O(13^2))*T^3 + (10 + 13 + O(13^2))*T^4 + O(T^5) sage: s = f[0] sage: s = s * E.torsion_order()^2 / E.tamagawa_product() sage: s/ ( 1-1/l.alpha() )^2 1 + O(13^5) Tough if you change 100 for a larger square it will quickly become very slow without using the twist (which is exactly was is broken here). Final note. The valuation part of the p-adic BSD actually holds although it is not implemented here (since E has complex multiplication). These computations prove that the 13-torsion part of Sha is trivial. Chris. -- 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 http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
