On the p-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication by the ring of integers of ℚ(√(-3))

2016/05/26 by Kezuka, Yukako
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1605.08245

Abstract

We study infinite families of quadratic and cubic twists of the elliptic curve E = X₀(27). For the family of quadratic twists, we establish a lower bound for the 2-adic valuation of the algebraic part of the value of the complex L-series at s=1, and, for the family of cubic twists, we establish a lower bound for the 3-adic valuation of the algebraic part of the same L-value. We show that our lower bounds are precisely those predicted by the celebrated conjecture of Birch and Swinnerton-Dyer.

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