Root number of twists of an elliptic curve
Journal de théorie des nombres de Bordeaux, Volume 32 (2020) no. 1, pp. 73-101.

We give an explicit description of the behaviour of the root number in the family given by the twists of an elliptic curve E/ by the rational values of a polynomial f(T). In particular, we present a criterion for the family to have a constant root number over . This completes work by Rohrlich: we detail the behaviour of the root number when E has bad reduction over ab and we treat the cases j(E)=0,1728 which were not considered previously.

Nous donnons une description explicite du comportement du signe (root number) dans la famille des tordues d’une courbe elliptique E/ par les valeurs rationnelles d’un polynôme f(t). En particulier, nous présentons un critère pour que la famille ait un signe constant sur . Ceci complète un travail de Rohrlich  : nous donnons les détails du comportement du signe lorsque E a mauvaise réduction sur ab et nous traitons les cas j(E)=0,1728 qui n’étaient pas considérés précédemment.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1112
Classification: 11G05, 11G07
Keywords: elliptic curve, root number, twist
Julie Desjardins 1

1 DH-3062, University of Toronto Mississauga 3359 Mississauga Road Mississauga, ON L5L 1C6, Canada
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Julie Desjardins. Root number of twists of an elliptic curve. Journal de théorie des nombres de Bordeaux, Volume 32 (2020) no. 1, pp. 73-101. doi : 10.5802/jtnb.1112. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1112/

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