Item Details

title

Torsion Points on Q-Curves in Least Odd Degree

author

Ryalls, Nina

abstract

In order to answer the question of which isogeny classes containing non-CM $\Q$-curves give rise to sporadic points of order $p^2$, we investigate within certain isogeny classes. In particular, for a point of order $p^k$ for a prime $p \in \{2,3,5,7,11,13\}$ defined over a number field $F$ of odd degree, we improve on existing bounds upon the degree of $F$ and prove our bounds are the best possible by exhibiting families of isogenous elliptic curves which have points of order $p^k$ defined over fields of lowest possible degree. Additionally, we prove analogous results for when the degree of $F$ is even and $p = 7$ or $5$.

contributor

Bourdon, Abbey (committee chair)

Rouse, Jeremy (committee member)

Kirkman, Ellen (committee member)

Bourdon, Abbey (committee member)

date

2022-05-24T08:36:03Z (accessioned)

2022-05-24T08:36:03Z (available)

2022 (issued)

degree

Mathematics and Statistics (discipline)

identifier

http://hdl.handle.net/10339/100738 (uri)

language

en (iso)

publisher

Wake Forest University

type

Thesis