#11095: Add BMSS algorithm for isogenies of elliptic curves
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Reporter: defeo | Owner: cremona
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-4.7.1
Component: elliptic curves | Keywords: isogenies
Work_issues: | Upstream: N/A
Reviewer: John Cremona | Author: Luca De Feo
Merged: | Dependencies:
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Changes (by defeo):
* status: needs_review => needs_work
Comment:
I realized that my code for BMSS fails when the isogeny has strictly
positive valuation at x, which happens for example when the origin is a
point of order 2 and the isogeny has odd degree as in the code below
{{{
sage: from sage.schemes.elliptic_curves.ell_isogeny_char_zero import *
sage: E = EllipticCurve([-1,0])
sage: E2 = EllipticCurve([-3^4,0])
sage: E.isogeny(kernel=None, codomain=E2, degree=9)
Traceback (most recent call last)
...
ValueError: The two curves are not linked by a normalized isogeny of
degree 9
sage: isogeny_Stark(E,E2,9)
x^8 - 4*x^6 + 10/3*x^4 + 4/3*x^2 + 1/9
sage: isogeny_BMSS(E,E2,9)
x^7 - 4*x^5 + 10/3*x^3 + 4/3*x
}}}
The fix is easy, I hope I'll have time to send a revised patch next week.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11095#comment:6>
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