Curvas elípticas e números congruentes

• Ano de defesa: 2013
• Autor(a) principal: Souza, Bruno Andrade de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; BR; Programa de Pós-graduação em Matemática; Ciências Exatas e da Terra; UFU
• Palavras-chave em Português: Curvas elípticas; Teorema de Mordel; Números congruentes; Elliptic curves; Mordell Theorem; Congruent numbers; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufu.br/handle/123456789/16800; https://doi.org/10.14393/ufu.di.2013.82

The aim of this paper is to relate Congruent Numbers and Elliptic Curves. We describe an operation on the curve, which makes the set of its points, on any field, an abelian group. Next we present the Nagell-Lutz theorem, which gives us the necessary conditions for a point that has finite order in the group. Having done this, we prove the Mordell theorem for curves like y2=x3+ax2+bx; this theorem tells us that the set of rational points on elliptic curve is a finitely generated abelian group. Finally, we define congruent numbers, we present some properties and examples of such numbers and establish the connection between Congruent Numbers and Elliptic Cuves.