This thesis examines the rank of elliptic curves. We first examine the correspondences between projective space and affine space, and use the projective point at infinity to establish the group law on elliptic curves. We prove a section of Mordell’s Theorem to establish that the abelian group of rational points on an elliptic curve is finitely generated. We then use homomorphisms established in our proof to find a formula for the rank, and then provide examples of computations.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:scripps_theses-1353 |
| Date | 18 May 2013 |
| Creators | Layden, Tracy |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Scripps Senior Theses |
| Rights | © 2013 Tracy Layden |
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