#11347: global_minimal_model function is sometimes wrong over number fields,
when
input model isn't integral.
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Reporter: was | Owner: cremona
Type: defect | Status: new
Priority: critical | Milestone: sage-4.7.1
Component: elliptic curves | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Description changed by was:
Old description:
> The discriminant and conductor of a global minimal model must be
> divisible by the same primes. However the following code (extracted from
> examples computed by Joanna Gaski), illustrates the Sage
> {{{global_minimal_model}}} function producing a model that can't possibly
> be a global minimal model (since the conductor and discriminant are
> divisible by different primes).
>
> {{{
> sage: E = EllipticCurve(K,[0,0,0,-1/48,161/864]).global_minimal_model();
> E
> Elliptic Curve defined by y^2 = x^3 + (-1)*x^2 + 12 over Number Field in
> g with defining polynomial x^2 - x - 1
> sage: E.conductor().factor()
> (Fractional ideal (3)) * (Fractional ideal (-2*g + 1))
> sage: E.discriminant().factor()
> (-1) * 2^12 * 3 * (-2*g + 1)^2
> }}}
> Again, the bug is that the global_minimal_model function is assuming that
> its input is integral, and the fix is easy, probably.
>
> {{{
> sage: E =
> EllipticCurve(K,[0,0,0,-1/48,161/864]).integral_model().global_minimal_model();
> E
> Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 over Number Field in
> g with defining polynomial x^2 - x - 1
> sage: E.conductor().factor()
> (Fractional ideal (3)) * (Fractional ideal (-2*g + 1))
> sage: E.discriminant().factor()
> (-1) * 3 * (-2*g + 1)^2
> }}}
>
> Yes, inspecting the source code shows a *typo* related to this, i.e.,
> somebody defines E to be a global integral model, then forgets to
> actually use E!
New description:
The discriminant and conductor of a global minimal model must be divisible
by the same primes. However the following code (extracted from examples
computed by Joanna Gaski), illustrates the Sage {{{global_minimal_model}}}
function producing a model that can't possibly be a global minimal model
(since the conductor and discriminant are divisible by different primes).
{{{
sage: K.<g> = NumberField(x^2 - x - 1)
sage: E = EllipticCurve(K,[0,0,0,-1/48,161/864]).global_minimal_model(); E
Elliptic Curve defined by y^2 = x^3 + (-1)*x^2 + 12 over Number Field in g
with defining polynomial x^2 - x - 1
sage: E.conductor().factor()
(Fractional ideal (3)) * (Fractional ideal (-2*g + 1))
sage: E.discriminant().factor()
(-1) * 2^12 * 3 * (-2*g + 1)^2
}}}
Again, the bug is that the global_minimal_model function is assuming that
its input is integral, and the fix is easy, probably.
{{{
sage: E =
EllipticCurve(K,[0,0,0,-1/48,161/864]).integral_model().global_minimal_model();
E
Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 over Number Field in g
with defining polynomial x^2 - x - 1
sage: E.conductor().factor()
(Fractional ideal (3)) * (Fractional ideal (-2*g + 1))
sage: E.discriminant().factor()
(-1) * 3 * (-2*g + 1)^2
}}}
Yes, inspecting the source code shows a *typo* related to this, i.e.,
somebody defines E to be a global integral model, then forgets to actually
use E!
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11347#comment:2>
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