#18589: isogeny efficiency improvement
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Reporter: cremona | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: elliptic curves | Keywords: isogeny
Merged in: | Authors: John Cremona
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Computation of isogenies of prime degree p is expensive when the degree is
neither a "genus zero" prime [2,3,5,7,13] or a "hyperelliptic prime" [11,
17, 19, 23, 29, 31, 41, 47, 59, 71] (for these there is special code
written). In one situation we can save time, after factoring the degree
(p^2-1)/2 division polynomial, if there is exactly one factor of degree
(p-1)/2, or one subset of factors whose product has that degree, then the
factor of degree (p-1)/2 must be a kernel polynomial. Then we do not need
to check consistency, which is very expensive.
The example which led me to this was with p=89 over a quadratic number
field, where E.isogeny_class() was taking days. After the change here
that goes down to 3 hours. (There are 4 curves in the isogeny class and
thec ode requires factoring the 89-division polynomial of each!) I will
find a less extreme example for a doctest.
--
Ticket URL: <http://trac.sagemath.org/ticket/18589>
Sage <http://www.sagemath.org>
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