A divisibility related to the Birch and Swinnerton-Dyer conjecture
نویسندگان
چکیده
Let E/Q be an optimal elliptic curve of analytic rank zero. It follows from the Birch and Swinnerton-Dyer conjecture for curves zero that order torsion subgroup divides product Shafarevich–Tate group E/Q, (global) Tamagawa number at infinity. This consequence was noticed by Agashe Stein in 2005. In this paper, we prove divisibility statement unconditionally many cases, including case where is semi-stable.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2023
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2022.10.004