Number Theory Commons^™

Counting Elliptic Curves With A Cyclic M-Isogeny Over Q, Grant S. Molnar

Dartmouth College Ph.D Dissertations

Using methods from analytic number theory, for m > 5 and for m = 4, we obtain asymptotics with power-saving error terms for counts of elliptic curves with a cyclic m-isogeny up to quadratic twist over the rational numbers. For m > 5, we then apply a Tauberian theorem to achieve asymptotics with power saving error for counts of elliptic curves with a cyclic m-isogeny up to isomorphism over the rational numbers.