#19229: Bug in elliptic curve Galois Representation
-------------------------------+------------------------------------------
Reporter: cremona | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.9
Component: elliptic curves | Keywords: Galois representations
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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{{{
sage: K.<a> = NumberField(x^2-x+1)
sage: E = EllipticCurve([a+1,1,1,0,0])
sage: C = IsogenyClass_EC_NumberField(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!)
--
Ticket URL: <http://trac.sagemath.org/ticket/19229>
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