#15434: elliptic curve isogenies: follow-up to #13615
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Reporter: cremona | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.13
Component: elliptic curves | Keywords:
Merged in: | Authors: John Cremona
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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In #13615 there were major enhancements to the ability to compute
isogenies of low degree for elliptic curves. A small bug was found after
the ticket was closed and the patched merged into 5.13.beta0:
{{{
sage: K.<i> = NumberField(x^2+1)
sage: E = EllipticCurve(K,[-2*i-1,0])
sage: E.isogenies_prime_degree(17)
...
ValueError: The polynomial does not define a finite subgroup of the
elliptic curve.
}}}
while in fact this curve does have 2 17-isogenies:
{{{
sage: from sage.schemes.elliptic_curves.isogeny_small_degree import
isogenies_prime_degree_general
sage: isogenies_prime_degree_general(E,17) # rather slow
[Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 +
(-2*i-1)*x over Number Field in i with defining polynomial x^2 + 1 to
Elliptic Curve defined by y^2 = x^3 + (-82*i-641)*x over Number Field in i
with defining polynomial x^2 + 1,
Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 +
(-2*i-1)*x over Number Field in i with defining polynomial x^2 + 1 to
Elliptic Curve defined by y^2 = x^3 + (-562*i+319)*x over Number Field in
i with defining polynomial x^2 + 1]
}}}
This was found by Warwick undergraduate Warren Moore.
This problem can be fixed as follows: in line 1770 of
isogeny_small_degree.py replace -27*c4 by -27*c4/1296 (or -c4/48) twice.
--
Ticket URL: <http://trac.sagemath.org/ticket/15434>
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