Stanley Xiao, University of Northern British Columbia
Elliptic curves admitting a rational isogeny of prime degree, ordered by conductor
We consider explicit parametrizations of rational points on the modular curves X_0(p) for p in {2,3,5,7}, which corresponds to elliptic curves E/Q$ admitting a rational isogeny of degree p, and consider conductor polynomials of such curves. Conductor polynomials are polynomial divisors of the discriminant which more closely approximate the conductors of elliptic curves. By using results on almost-prime values of polynomials, including recent breakthrough work of Ben Green and Mehtaab Sawhney, we count such curves whose conductors have the least number of distinct prime factors, ordered by conductor. This is joint work with Alia Hamieh and Fatma Cicek.
MC 5417