| LDR | | 02180nmm uu200409 4500 |
| 001 | | 000000332870 |
| 005 | | 20240805171737 |
| 008 | | 181129s2018 |||||||||||||||||c||eng d |
| 020 | |
▼a 9780438010307 |
| 035 | |
▼a (MiAaPQ)AAI10808913 |
| 035 | |
▼a (MiAaPQ)purdue:22733 |
| 040 | |
▼a MiAaPQ
▼c MiAaPQ
▼d 248032 |
| 082 | 0 |
▼a 510 |
| 100 | 1 |
▼a Barrios, Alexander J. |
| 245 | 10 |
▼a Minimal Models of Rational Elliptic Curves with Non-trivial Torsion. |
| 260 | |
▼a [S.l.] :
▼b Purdue University.,
▼c 2018 |
| 260 | 1 |
▼a Ann Arbor :
▼b ProQuest Dissertations & Theses,
▼c 2018 |
| 300 | |
▼a 372 p. |
| 500 | |
▼a Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B. |
| 500 | |
▼a Adviser: Edray H. Goins. |
| 502 | 1 |
▼a Thesis (Ph.D.)--Purdue University, 2018. |
| 520 | |
▼a This dissertation concerns the formulation of an explicit modified Szpirobconjecture and the classification of minimal discriminants of rational elliptic curves with non-trivial torsion subgroup. |
| 520 | |
▼a The Frey curve y2=x( x+a) ( x-b) is a two-parameter family of elliptic curves which comes equipped with an easily computable minimal discriminant which helped pave the mathematical bridge that led to the proof of Fermat's Last Theorem. In this |
| 520 | |
▼a The second theme of this dissertation concerns the modified Szpiro conjecture, which is equivalent to the ABC Conjecture. Roughly speaking, the modified Szpiro conjecture states that certain elliptic curves, known as good elliptic curves, are ra |
| 520 | |
▼a Lastly, we use the classification of minimal discriminants to study the local data of rational elliptic curves at a given prime via Tate's Algorithm. These results and a study of the naive height of an elliptic curve allow us to prove that there |
| 590 | |
▼a School code: 0183. |
| 650 | 4 |
▼a Mathematics. |
| 690 | |
▼a 0405 |
| 710 | 20 |
▼a Purdue University.
▼b Mathematics. |
| 773 | 0 |
▼t Dissertation Abstracts International
▼g 79-10B(E). |
| 773 | |
▼t Dissertation Abstract International |
| 790 | |
▼a 0183 |
| 791 | |
▼a Ph.D. |
| 792 | |
▼a 2018 |
| 793 | |
▼a English |
| 856 | 40 |
▼u http://www.riss.kr/pdu/ddodLink.do?id=T14997845
▼n KERIS |
| 980 | |
▼a 201812
▼f 2019 |
| 990 | |
▼a 관리자 |