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handle: 2099.1/19368
This thesis deals primarily with the question of finding equations for bielliptic modular curves of the type $X_{0}(N)$. After introducing the reader to some of the fundamental aspects on the theory modular curves, we discuss four different techniques for finding such models and give examples of their implementation in Sage.. Es tracta d'estudiar les corbes modulars biel.líptiques, determinades per F. Bars en l'article Bielliptic Modular curves [1999], amb l'objectiu de trobar equacions i, en el cas, que aquestes tenen quocients el.líptics amb rang major que 1, donar una parametrització dels discriminants del cossos quadràtics on les corbes modulars tenen definits punts sobre aquets.
Atkin-Lehner theory, Geometria algèbrica--Aritmètica, Modularity theorem, Newman's group, :11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) [Classificació AMS], modular forms, Arithmetical algebraic geometry, :Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC], Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry), Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres, bielliptic modular curves
Atkin-Lehner theory, Geometria algèbrica--Aritmètica, Modularity theorem, Newman's group, :11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) [Classificació AMS], modular forms, Arithmetical algebraic geometry, :Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC], Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry), Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres, bielliptic modular curves
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