Voloch, José Felipe576860142008-08-282008-08-282004http://hdl.handle.net/2152/1294textLet us assume that E/Q is an elliptic curve of level N and rank equal to 1. Let q be a prime that does not divide the conductor. We study conjecture 4 of B. Mazur and J. Tate in [MT87]. This conjecture relates to the Birch and Swinnerton-Dyer problem in the q-adic case. We produce a lot of numerical evidence towards the conjecture. We also propose a refinement of the conjecture in the rank 1 case in section 2.3.electronicengCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.Birch-Swinnerton-Dyer conjectureMazur-Tate conjectureThesis3143450