Families of Rank Zero Twists of Elliptic Curves

The objective of this thesis is to generalize this result to a bigger class of elliptic curves. We are going to generalize Serf's result to the family of elliptic curves with full 2-torsion, i.e. elliptic curves of the form $E:y\sp2 = (x-e\sb1)(x-e\sb2)(x-e\sb3)$ with $e\sb{i}\in\doubz.$ We can also assume that $e\sb1 = 0$ and that $e\sb2$ and $e\sb3$ are both odd.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Iskra, Boris

Contributors dc:contributor

• Boston, Nigel

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9904488

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86961