#19229: Bug in elliptic curve Galois Representation
-------------------------------------+-------------------------------------
Reporter: cremona | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.9
Component: elliptic curves | Resolution:
Keywords: Galois | Merged in:
representations | Reviewers:
Authors: John Cremona | Work issues:
Report Upstream: N/A | Commit:
Branch: u/cremona/19229 | df3d3f7c5819198be47c0f3dc8d7419066cee34c
Dependencies: | Stopgaps:
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Description changed by cremona:
Old description:
> {{{
> sage: K.<a> = NumberField(x^2-x+1)
> sage: E = EllipticCurve([a+1,1,1,0,0])
> sage: C = E.isogeny_class(E)
> ...
> ValueError: 0 is not prime.
> }}}
> is caused by
> {{{
> sage: from sage.schemes.elliptic_curves.isogeny_class import
> possible_isogeny_degrees
> sage: possible_isogeny_degrees(E)
> [0]
> }}}
> and in turn by
> {{{
> sage: EG = E.galois_representation()
> sage: EG.reducible_primes()
> [0]
> }}}
>
> According to the documentation for the last function it should return [0]
> if and only if E has CM, which is does not:
> {{{
> sage: E.has_cm()
> False
> sage: E.j_invariant().is_integral()
> False
> }}}
> (CM curves certainly have integral j-invariant, so you don't need to
> trust the is_cm() method to believe that!)
New description:
{{{
sage: K.<a> = NumberField(x^2-x+1)
sage: E = EllipticCurve([a+1,1,1,0,0])
sage: C = E.isogeny_class()
...
ValueError: 0 is not prime.
}}}
is caused by
{{{
sage: from sage.schemes.elliptic_curves.isogeny_class import
possible_isogeny_degrees
sage: possible_isogeny_degrees(E)
[0]
}}}
and in turn by
{{{
sage: EG = E.galois_representation()
sage: EG.reducible_primes()
[0]
}}}
According to the documentation for the last function it should return [0]
if and only if E has CM, which is does not:
{{{
sage: E.has_cm()
False
sage: E.j_invariant().is_integral()
False
}}}
(CM curves certainly have integral j-invariant, so you don't need to trust
the is_cm() method to believe that!)
--
--
Ticket URL: <http://trac.sagemath.org/ticket/19229#comment:5>
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