Watkins's conjecture for quadratic twists of Elliptic Curves with Prime Power Conductor

2022/06/20 by Caro, Jerson
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2206.10008

Abstract

Watkins' conjecture asserts that the rank of an elliptic curve is upper bounded by the 2-adic valuation of its modular degree. We show that this conjecture is satisfied when E is any quadratic twist of an elliptic curve with rational 2-torsion and prime power conductor. Furthermore, we give a lower bound of the congruence number for elliptic curves of the form y²=x³-dx, with d a biquadratefree integer.

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