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arXiv · 1010.0732

On Quadratic Twists of Hyperelliptic Curves

Mohammad Sadek
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Abstract

Let C be a hyperelliptic curve of good reduction defined over a discrete valuation field K with algebraically closed residue field k. Assume moreover that char k \ne 2. Given d \in K^*\K^*2, we introduce an explicit description of the minimal regular model of the quadratic twist of C by d. As an application, we show that if C/Q is a nonsingular hyperelliptic curve given by y^2 = f(x) with f an irreducible polynomial, there exists a positive density family of prime quadratic twists of C which are not everywhere locally soluble.

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BibTeXRIS

Mohammad Sadek. 2010-10-04. On Quadratic Twists of Hyperelliptic Curves. https://arxiv.org/abs/1010.0732

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