Chowdhury, Syed Hasibul HassanChowdhury, Atonu Roy2025-06-222025-06-2220252025-01ID 20216008http://hdl.handle.net/10361/26143This thesis is submitted in partial fulfilment of the requirements for the degree of Bachelor of Science in Mathematics, 2025.Catalogued from the PDF version of thesis.Includes bibliographical references (page 39).This thesis investigates the interplay between the morphism spaces of elliptic curves and their associated Tate modules. Specifically, we focus on proving the injectivity of the map Hom (E1,E2) ⊗ Zp → Hom (Tp (E1) , Tp (E2)) , where E1 and E2 are elliptic curves, and Tp (E) denotes the p-adic Tate module associated with the elliptic curve E. The result connects the algebraic structure of morphisms over elliptic curves with the module-theoretic properties of their Tate modules. We employ tools from algebraic geometry and p-adic number theory, focusing on the role of endomorphism rings and Tate modules. This work contributes to understanding how information about elliptic curve morphisms is preserved and reflected in the realm of p-adic arithmetic.39 pagesenBRAC University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission.Elliptic curvesTate modulep-adic arithmeticAlgebraic geometryHomomorphismsHomomorphisms (Mathematics).p-adic analysis.Geometry, Algebraic.Curves, Elliptic.Thesis