Noam Elkies


Harvard University


Sunday, November 4, 2012 - 11:30am to 12:30pm


DBH 1600

On the occasion of the creation of a table of modular elliptic curves over Q(sqrt(5)), we review the "Remarks on isogenies" that accompanied the "Antwerp" tables (LNM 476), and outline some of the new phenomena and open questions that arise in attempting to give a similar overview of isogenies defined over Q(sqrt(5)) or other number fields. In particular, we account for some new isogeny degrees and graphs not seen over Q, and explain why the problem of proving completeness of the list over Q(sqrt(5)) is difficult but not hopeless.