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].
Citation
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
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