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November 2021 Elliptic curves with all quartic twists of the same root number
Dongho Byeon, Gyeoul Han
Proc. Japan Acad. Ser. A Math. Sci. 97(9): 73-75 (November 2021). DOI: 10.3792/pjaa.97.014

Abstract

Let $E/K$ be an elliptic curve with $j$-invariant 1728 defined over a number field $K$. In this note, we give a simple condition on $K$ which determines whether all quartic twists of $E/K$ have the same root number or not. This completes a series of works on the same root number of twists begun in [DD1] and [BK].

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Dongho Byeon. Gyeoul Han. "Elliptic curves with all quartic twists of the same root number." Proc. Japan Acad. Ser. A Math. Sci. 97 (9) 73 - 75, November 2021. https://doi.org/10.3792/pjaa.97.014

Information

Published: November 2021
First available in Project Euclid: 4 November 2021

Digital Object Identifier: 10.3792/pjaa.97.014

Subjects:
Primary: 11G05
Secondary: 11G07

Keywords: Elliptic curve , quartic twist , root number

Rights: Copyright © 2021 The Japan Academy

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Vol.97 • No. 9 • November 2021
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