Implementing an algorithm for contructing genus 2 hyperelliptic curves with extra automorphism

[sagetrac-florian]

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 Cardona and Quer

Depends on #6341

CC: @mstreng

Component: number theory

Keywords: mestre algorithm genus 2 hyperelliptic curves

Issue created by migration from https://trac.sagemath.org/ticket/12199

[sagetrac-florian]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-Mestre's algorithm for constructing hyperelliptic curves has been implemented see tickect #6341 but it only works for generic curve.
+Mestre's algorithm for constructing hyperelliptic curves has been implemented see ticket #6341 but it only works for generic curve.
 
 ```
     .. TODO::

[mstreng]

Dependencies: #6341

[mstreng]

Changed keywords from Hyperelliptic curve to Hyperelliptic curve sd35

[mstreng]

Description changed:

--- 
+++ 
@@ -10,3 +10,5 @@
         sage: HyperellipticCurve_from_invariants(C.igusa_clebsch_invariants()) # todo: not implemented
     
 ```
+
+The missing case can be taken from the article of [Cardona and Quer](http://arxiv.org/abs/math/0207015)

[mstreng]

Changed keywords from Hyperelliptic curve sd35 to mestre algorithm genus 2 hyperelliptic curves sd51

[mstreng]

Changed keywords from mestre algorithm genus 2 hyperelliptic curves sd51 to mestre algorithm genus 2 hyperelliptic curves