Item Details

abstract

An elliptic curve E over Q corresponds to an equation of the form y2 = x^3+ax+b fora,b in Q. Points on E form an abelian group under a specific group operation. The modular curve X1(N) parametrizes pairs [E,P], where P is a point of order N on an elliptic curve E. A point [E,P] in X1(N) is called isolated if it does not belong to an infinite family of points of the same degree. Isogeny class 162.c is a family of four elliptic curves that are related in a natural way by rational maps called isogenies. We investigate the curves in this family. Let [E,P] in X1(N) be an isolated point of odd degree on the modular curve X1(N), corresponding to an elliptic curve in class 162.c. We show that E must be the elliptic curve y2 = x^3-6075x+190998.

subject

contributor

Gill, David R. (author)

Bourdon, Abbey (committee chair)

Robinson, Stephen (committee member)

Rouse, Jeremy (committee member)

date

2021-01-13T09:35:20Z (accessioned)

2021-01-13T09:35:20Z (available)

2020 (issued)

degree

Mathematics and Statistics (discipline)

identifier

http://hdl.handle.net/10339/97951 (uri)

language

en (iso)

publisher

Wake Forest University

title

Isolated Points with Rational j-Invariant in an Isogeny Class of Elliptic Curves

type

Thesis