Modular curves of genus one and their associated period lattices

Nomden, Stef (2023) Modular curves of genus one and their associated period lattices. Bachelor's Thesis, Mathematics.

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Abstract

In this thesis we construct modular elliptic curves associated to modular curves X0(N) of genus one. We introduce the notion of a Riemann surface and we study modular curves in this context. We study holomorphic differentials on modular curves and relate these to the set of cusp forms. We write down generators of S2(Γ0(N)) which are realised as eta-products and use these to calculate the period lattices associated to X0(N). The theory of elliptic functions is developed and used to construct an elliptic curve from a period lattice. Finally, we put this theory together to compute the elliptic curves which are isomorphic to X0(N).

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Muller, J.S. and Salgado Guimaraes da Silva, C.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	24 Jul 2023 07:21
Last Modified:	24 Jul 2023 07:21
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/30816

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