Numerical study of refined conjectures of the BSD type

Abstract

In 1987, Mazur and Tate stated conjectures which, in some cases, resemble the classical Birch-Swinnerton-Dyer conjecture and its $p$-adic analog. We study experimentally three conjectures stated by Mazur and Tate using SageMath. Our findings indicate discrepancies in some of the original statements of some of the conjectures presented by Mazur and Tate. However, a slight modification on the statement of these conjectures does appear to hold.

The function f in Lemma 1.1 was, at best, an abuse of notation, but strictly speaking not well-defined. Thus, we corrected the isomorphism. This does not affect Remark 1.5. Also, fix some typos. 15 pages. For associated code, see: https://github.com/JpLlerena/Numerical_study_of_refined_conjectures_of_the_BSD-type