Tom Womack on Wed, 7 Jun 2000 15:38:04 +0100

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Computing analytic ranks

I've written some code for computing analytic ranks of elliptic curves using
the Buhler-Gross recursive method for computing sums of multiplicative
functions. You can download it from

and there's some test code in

I hope the comments are enough to make it self-explanatory: it implements
the functions

ellanalyticrank(e) = [rank, L^(rank)(1), regulator*sha from BSD-conjecture]

ellRegSha(e,r) [where r is the rank of e] = regulator*sha from

ellSha(e, [pts]) takes a set of points supposed to generate e, and computes
the analytic value of sha.

I've been fairly careful that my global variables have peculiar names, so
this should co-exist reasonably with other packages.