Parity of ranks for elliptic curves with a cyclic isogeny

Tim Dokchitser; Vladimir Dokchitser

doi:10.1016/j.jnt.2007.02.008

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Parity of ranks for elliptic curves with a cyclic isogeny

Tim Dokchitser·Vladimir Dokchitser

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Abstract

Let E be an elliptic curve over a number field K which admits a cyclic p-isogeny with p odd and semistable at primes above p. We determine the root number and the parity of the p-Selmer rank for E/K, in particular confirming the parity conjecture for such curves. We prove the analogous results for p=2 under the additional assumption that E is not supersingular at primes above 2.

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Tim Dokchitser, Vladimir Dokchitser. 2007-04-09. Parity of ranks for elliptic curves with a cyclic isogeny. https://doi.org/10.1016/j.jnt.2007.02.008

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