Some comments, especially on the Sage code you sent me a link to.

1. Sage's long-existing E.isogenies_prime(degree(ell)  works fine for
ell=2,3,5,7,13 over any number field, so you should be using that for
those ell.

2. The division-polynomial code you have is wrong, and will miss some
isogenies.  You want a factor of the div. poly. of degree (l-1)/2, but
it does not have to be an irreducible factor, and not every
irreducible factor of that degree will be valid.  (For example, when
ell=5 it is possible that the two x-coordinates in the subgroup are
both in your field, so you'll have two degree-1 factors and not one
degree-2).  I explained how to deal with this in my talk at MSRI a
year ago.  I suggest that your students look at that talk, and I will
send you Kimi's code which takes the factors of the division poly and
does the right thing with them.

3. Kimi is about to go away for 3 weeks, but he has just given me his
code for ell=11, which will also work for ell=17 and 19 at least,
though possibly not for curves with j=0 and j=1728.  (However it is a
fact that there are no 11-isogenies when j=0 or j=1728 over a
quadratric field anyway).  I will check those out and send them to you
right away.

John