#11639: conductor of simple curve over Q(cube root 3) takes forever
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Reporter: was | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.2
Component: elliptic curves | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by fwclarke):
This is the heart of the problem
{{{
sage: K.<a> = NumberField(x^3 - 2); E = EllipticCurve([0, a])
sage: P, Q = K.prime_factors(E.discriminant())
sage: P, P.gens()
(Fractional ideal (a), (2, a))
sage: P2 = P*P; P2, P2.gens()
(Fractional ideal (a^2), (4, 2*a, 2*a, a^2))
}}}
The conductor is computed as `P^14*Q^9`, which is defined by 2^23^ (highly
redundant) generators. Multiplication of ideals avoids reducing the
generators, which can be time-consuming (though not in this case), but it
could at least eliminate repeats.^^
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11639#comment:2>
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