#13615: Extend elliptic curve isogenies to arbitrary prime degrees
-------------------------------------+-------------------------------------
Reporter: cremona | Owner: John Cremona
Type: enhancement | Status: closed
Priority: major | Milestone: sage-5.13
Component: elliptic curves | Resolution: fixed
Keywords: isogenies, sd51, | Merged in: sage-5.13.beta0
sd52 | Reviewers: John Cremona, Jenny
Authors: Kimi Tsukazaki, | Cooley, Samuele Anni, Luca De Feo
John Cremona, Luca De Feo | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by cremona):
We have a problem, which I am investigating:
{{{
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, and I am looking
into it....
--
Ticket URL: <http://trac.sagemath.org/ticket/13615#comment:50>
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