The Birch--Swinnerton-Dyer exact formula for quadratic twists of elliptic curves

2021/02/23 by Zhai, Shuai
#11F67 #11G05 #11G40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2102.11798

Abstract

In the present short paper, we obtain a general lower bound for the 2-adic valuation of the algebraic part of the central value of the complex L-series for the quadratic twists of any elliptic curve E over ℚ. We also prove the existence of an explicit infinite family of quadratic twists with analytic rank 0 for a large family of elliptic curves.

Related

• On the p-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication by the ring of integers of ℚ(√(-3))
• On the 2-part of the Birch and Swinnerton-Dyer conjecture for quadratic twists of elliptic curves
• Non-vanishing Theorems for Quadratic Twists of Elliptic Curves
• On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication
• Generalized Birch lemma and the 2-part of the Birch and Swinnerton-Dyer conjecture for certain elliptic curves