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Published online by Cambridge University Press:  09 July 2019

School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China email
School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, PR China email


Let $p$ be an odd prime number and $E$ an elliptic curve defined over a number field $F$ with good reduction at every prime of $F$ above $p$. We compute the Euler characteristics of the signed Selmer groups of $E$ over the cyclotomic $\mathbb{Z}_{p}$-extension. The novelty of our result is that we allow the elliptic curve to have mixed reduction types for primes above $p$ and mixed signs in the definition of the signed Selmer groups.

Research Article
© 2019 Australian Mathematical Publishing Association Inc.

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M. F. Lim is supported by the National Natural Science Foundation of China under Grant Nos. 11550110172 and 11771164.


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