Krause, Elliot, authorAchter, Jeffrey, advisorPries, Rachel, committee memberJuul, Jamie, committee memberRay, Indrajit, committee member2023-01-212023-01-212022https://hdl.handle.net/10217/236044Let E be an ordinary elliptic curve over a prime field Fp. Attached to E is the characteristic polynomial of the Frobenius endomorphism, T2 − a1T + p, which controls several of the invariants of E, such as the point count and the size of the isogeny class. As we base change E over extensions Fpn, we may study the distribution of point counts for both of these invariants. Additionally, we look to quantify the rate at which these distributions converge to the expected distribution. More generally, one may consider these same questions for collections of ordinary elliptic curves and abelian varieties.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.elliptic curveabelian varietiesText