Sage: Ticket #15434: elliptic curve isogenies: follow-up to #13615
https://trac.sagemath.org/ticket/15434
<p>
In <a class="closed ticket" href="https://trac.sagemath.org/ticket/13615" title="enhancement: Extend elliptic curve isogenies to arbitrary prime degrees (closed: fixed)">#13615</a> there were major enhancements to the ability to compute isogenies of low degree for elliptic curves. A small bug was found after the ticket was closed and the patched merged into 5.13.beta0:
</p>
<pre class="wiki">sage: K.<i> = NumberField(x^2+1)
sage: E = EllipticCurve(K,[-2*i-1,0])
sage: E.isogenies_prime_degree(17)
...
ValueError: The polynomial does not define a finite subgroup of the elliptic curve.
</pre><p>
while in fact this curve does have 2 17-isogenies:
</p>
<pre class="wiki">sage: from sage.schemes.elliptic_curves.isogeny_small_degree import isogenies_prime_degree_general
sage: isogenies_prime_degree_general(E,17) # rather slow
[Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + (-2*i-1)*x over Number Field in i with defining polynomial x^2 + 1 to Elliptic Curve defined by y^2 = x^3 + (-82*i-641)*x over Number Field in i with defining polynomial x^2 + 1,
Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + (-2*i-1)*x over Number Field in i with defining polynomial x^2 + 1 to Elliptic Curve defined by y^2 = x^3 + (-562*i+319)*x over Number Field in i with defining polynomial x^2 + 1]
</pre><p>
This was found by Warwick undergraduate Warren Moore.
</p>
<p>
This problem can be fixed as follows: in line 1770 of isogeny_small_degree.py replace -27*c4 by -27*c4/1296 (or -c4/48) twice.
</p>
en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/15434
Trac 1.1.6cremonaMon, 18 Nov 2013 13:00:37 GMTstatus changed
https://trac.sagemath.org/ticket/15434#comment:1
https://trac.sagemath.org/ticket/15434#comment:1
<ul>
<li><strong>status</strong>
changed from <em>new</em> to <em>needs_review</em>
</li>
</ul>
<p>
I checked that the problem does not also arise for the similar case of elliptic curves with j=0 over fields containing sqrt(-3) and primes =1 (mod 3).
</p>
TicketvbraunMon, 18 Nov 2013 13:27:59 GMTstatus changed; reviewer set
https://trac.sagemath.org/ticket/15434#comment:2
https://trac.sagemath.org/ticket/15434#comment:2
<ul>
<li><strong>status</strong>
changed from <em>needs_review</em> to <em>positive_review</em>
</li>
<li><strong>reviewer</strong>
set to <em>Volker Braun</em>
</li>
</ul>
TicketcremonaMon, 18 Nov 2013 13:36:03 GMT
https://trac.sagemath.org/ticket/15434#comment:3
https://trac.sagemath.org/ticket/15434#comment:3
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/15434#comment:2" title="Comment 2">vbraun</a>:
Thanks for looking at this so quickly!
</p>
TicketcremonaMon, 18 Nov 2013 20:37:03 GMTstatus changed
https://trac.sagemath.org/ticket/15434#comment:4
https://trac.sagemath.org/ticket/15434#comment:4
<ul>
<li><strong>status</strong>
changed from <em>positive_review</em> to <em>needs_work</em>
</li>
</ul>
<p>
Not so fast: my patch is not good on non-short Weierstrass models. Warren now reports this:
</p>
<pre class="wiki">sage: K.<i> = NumberField(x^2+1)
sage: E = EllipticCurve(K, [-2*i-1,0])
sage: E.isogenies_prime_degree(17)
[Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + (-2*i-1)*x over Number Field in i with defining polynomial x^2 + 1 to Elliptic Curve defined by y^2 = x^3 + (-82*i-641)*x over Number Field in i with defining polynomial x^2 + 1,
Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + (-2*i-1)*x over Number Field in i with defining polynomial x^2 + 1 to Elliptic Curve defined by y^2 = x^3 + (-562*i+319)*x over Number Field in i with defining polynomial x^2 + 1]
sage: E.global_minimal_model().isogenies_prime_degree(17)
<boom>
</pre>
TicketcremonaTue, 19 Nov 2013 13:18:22 GMTattachment set
https://trac.sagemath.org/ticket/15434
https://trac.sagemath.org/ticket/15434
<ul>
<li><strong>attachment</strong>
set to <em>trac_15434-bugfix.patch</em>
</li>
</ul>
<p>
applies to 5.13.beta3
</p>
TicketcremonaTue, 19 Nov 2013 13:19:43 GMTstatus changed
https://trac.sagemath.org/ticket/15434#comment:5
https://trac.sagemath.org/ticket/15434#comment:5
<ul>
<li><strong>status</strong>
changed from <em>needs_work</em> to <em>needs_review</em>
</li>
</ul>
<p>
The new patch does this properly now. The new changed line agree's with Kimi's thesis, and with the similar code for j=0, and I added another doctest with the minimal model (the first patch only worked when b2=0).
</p>
TicketvbraunTue, 19 Nov 2013 15:31:48 GMTstatus changed
https://trac.sagemath.org/ticket/15434#comment:6
https://trac.sagemath.org/ticket/15434#comment:6
<ul>
<li><strong>status</strong>
changed from <em>needs_review</em> to <em>positive_review</em>
</li>
</ul>
<p>
looks good to me
</p>
TicketjdemeyerFri, 22 Nov 2013 15:49:47 GMTstatus changed; resolution, merged set
https://trac.sagemath.org/ticket/15434#comment:7
https://trac.sagemath.org/ticket/15434#comment:7
<ul>
<li><strong>status</strong>
changed from <em>positive_review</em> to <em>closed</em>
</li>
<li><strong>resolution</strong>
set to <em>fixed</em>
</li>
<li><strong>merged</strong>
set to <em>sage-5.13.beta4</em>
</li>
</ul>
Ticket