Parity of ranks for elliptic curves with a cyclic isogeny

Details Parity of ranks for elliptic curves with a cyclic isogeny Parity of ranks for elliptic curves with a cyclic isogeny

2006-04-06

arxiv.org/abs/math/0604149v3

Mathematics

Number Theory

Minor corrections; 17 pages, to appear in J. Number Theory

Scientific paper

10.1016/j.jnt.2007.02.008

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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