Sage: Ticket #7368: Further work on isogenies and endomorphisms of elliptic curves
http://trac.sagemath.org/ticket/7368
<p>
Working on ticket <a class="closed ticket" href="http://trac.sagemath.org/ticket/7096" title="defect: bug in dual isogeny computation (closed: fixed)">#7096</a>, I realised that there are many functionalities concerning morphisms of elliptic curves that are not implemented or implemented badly.
</p>
<p>
See also <a class="closed ticket" href="http://trac.sagemath.org/ticket/6887" title="enhancement: Implement elliptic curve isogenies (continued) (closed: fixed)">#6887</a>, and <a class="closed ticket" href="http://trac.sagemath.org/ticket/7262" title="defect: Have multiplication_by_m() return an EllipticCurveIsogeny object (closed: fixed)">#7262</a>.
</p>
<p>
Here is a wish-list
</p>
<ul><li>General isogenies, not only cyclic ones should be implemented.
Possibly this could be done in a clever way, by having it
internally factored into cyclic isogenies.
</li><li>Non seperable isogenies, i.e. Frobenii should be there too. See
also <a class="new ticket" href="http://trac.sagemath.org/ticket/6413" title="defect: Retrieving the multiplication-by-p isogeny on elliptic curves over fields ... (new)">#6413</a>.
</li><li>One should be able to compose them -> see <a class="closed ticket" href="http://trac.sagemath.org/ticket/16245" title="defect: Compose isogenies (closed: fixed)">#16245</a>
</li><li>Is there a way of constructing a (not necessarily normalized)
isogeny knowing the degree and the domain and codomain ?
</li><li>There should be an addition for isogenies with the same domain
and codomain.
</li><li>There should be an endomorphism_ring for ellliptic curves whose
elements are isogenies.
</li><li>Similar automorphisms should give a group of isogenies.
</li></ul>en-usSagehttp://trac.sagemath.org/chrome/site/sage_logo_trac_v2.png
http://trac.sagemath.org/ticket/7368
Trac 1.1.1weigandtSat, 26 Mar 2011 06:32:19 GMTcc, upstream set
http://trac.sagemath.org/ticket/7368#comment:1
http://trac.sagemath.org/ticket/7368#comment:1
<ul>
<li><strong>cc</strong>
<em>weigandt</em> added
</li>
<li><strong>upstream</strong>
set to <em>N/A</em>
</li>
</ul>
TicketpbruinFri, 11 Apr 2014 11:05:26 GMTcc changed
http://trac.sagemath.org/ticket/7368#comment:2
http://trac.sagemath.org/ticket/7368#comment:2
<ul>
<li><strong>cc</strong>
<em>pbruin</em> added
</li>
</ul>
TicketsbesnierSat, 26 Apr 2014 19:59:54 GMTdescription changed
http://trac.sagemath.org/ticket/7368#comment:3
http://trac.sagemath.org/ticket/7368#comment:3
<ul>
<li><strong>description</strong>
modified (<a href="/ticket/7368?action=diff&version=3">diff</a>)
</li>
</ul>
TicketsbesnierSun, 27 Apr 2014 22:11:36 GMTcc changed
http://trac.sagemath.org/ticket/7368#comment:4
http://trac.sagemath.org/ticket/7368#comment:4
<ul>
<li><strong>cc</strong>
<em>sbesnier</em> added
</li>
</ul>
Ticket