Guitart Morales, XavierGarcía Pons, Rubén2022-04-252022-04-252021-06-20https://hdl.handle.net/2445/185152Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Xavier Guitart Morales[en] Elliptic curves play a very notable role in many number theory problems. In this work, we study the structure of the group of rational points of elliptic curves defined over the rationals. More specifically, we give a proof of Mordell’s Theorem and include some results to be able to present the Birch and Swinnerton-Dyer Conjecture.56 p.application/pdfcatcc-by-nc-nd (c) García Pons, Rubén, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Corbes el·líptiquesTreballs de fi de grauGeometria algebraica aritmèticaTeoria algebraica de nombresElliptic curvesBachelor's thesesArithmetical algebraic geometryAlgebraic number theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess