id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
21046,Numerical modular symbols for elliptic curves,wuthrich,,"I propose here to add fast modular symbols for elliptic curves. The proposed changes would add a cython file containing the new code to work with numerical modular symbols and integrate them for using for elliptic curves and their p-adic L-functions.
The idea is similar to #6666, where ""analytic modular symbols"" were added to elliptic curves. However the code there is very slow and this ticket would replace that code completely.
So a modular symbol for a given elliptic curve can be computed using numerical integration on the upper half plane rather than using linear algebra to determine the space of all modular symbols of level N first. Unlike #6666, we use rigorous bounds on the error of computations to be certain that we get the correct rational number.
The code here compares in speed with eclib and is wayway faster than the python code within sage. When computing a single modular symbol or a few with small denominator, the code here is much faster than eclib and can cope with conductors in the millions. When computing all manin symbols for one curve, the speed is in the same order as for eclib for semistable curves, but sometimes slower.
The preprint explaining all is [https://www.maths.nottingham.ac.uk/personal/cw/download/modsym.pdf here].",enhancement,closed,major,sage-9.1,elliptic curves,fixed,modular symbols,John Cremona Marc Masdeu William Stein Peter Bruin,,Chris Wuthrich,Varenyam Bakshi,N/A,,1a1a8ef6767c837428d04912bc4f7db79bfc058d,,,