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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-153
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:STANLEY XIAO\, UNIVERSITY OF NORTHERN BRITISH COLUMBIA\n\n_Elli
 ptic curves admitting a rational isogeny of prime degree\, ordered\nby con
 ductor_\n\nWe consider explicit parametrizations of rational points on the
 \nmodular curves X_0(p) for p in {2\,3\,5\,7}\, which corresponds to\nelli
 ptic curves E/Q$ admitting a rational isogeny of degree p\, and\nconsider 
 conductor polynomials of such curves. Conductor polynomials\nare polynomia
 l divisors of the discriminant which more closely\napproximate the conduct
 ors of elliptic curves. By using results on\nalmost-prime values of polyno
 mials\, including recent breakthrough work\nof Ben Green and Mehtaab Sawhn
 ey\, we count such curves whose\nconductors have the least number of disti
 nct prime factors\, ordered by\nconductor. This is joint work with Alia Ha
 mieh and Fatma Cicek. \n\nMC 5417
DTSTAMP:20260408T022756Z
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