Root number of the twists of an elliptic curve

2018/01/16 by Desjardins, Julie
#11G05 #11G07 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.05262

Abstract

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

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