#12199: Implementing an algorithm for contructing genus 2 hyperelliptic curves
with
extra automorphism
-----------------------------+----------------------------------------------
Reporter: florian | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: number theory | Keywords: Hyperelliptic curve sd35
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies: #6341
-----------------------------+----------------------------------------------
Description changed by mstreng:
Old description:
> Mestre's algorithm for constructing hyperelliptic curves has been
> implemented see ticket #6341 but it only works for generic curve.
>
> {{{
> .. TODO::
>
> Mestre's algorithm only works for generic curves of genus two, so
> an other algorithm is needed for those curves with extra automorphism
>
> sage: P.<x> = QQ[]
> sage: C = HyperellipticCurve(x^6+1)
> sage:
> HyperellipticCurve_from_invariants(C.igusa_clebsch_invariants()) # todo:
> not implemented
>
> }}}
New description:
Mestre's algorithm for constructing hyperelliptic curves has been
implemented see ticket #6341 but it only works for generic curve.
{{{
.. TODO::
Mestre's algorithm only works for generic curves of genus two, so
an other algorithm is needed for those curves with extra automorphism
sage: P.<x> = QQ[]
sage: C = HyperellipticCurve(x^6+1)
sage:
HyperellipticCurve_from_invariants(C.igusa_clebsch_invariants()) # todo:
not implemented
}}}
The missing case can be taken from the article of
[http://arxiv.org/abs/math/0207015 Cardona and Quer]
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12199#comment:3>
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