Parity of ranks for elliptic curves with a cyclic isogeny

DOI10.1016/j.jnt.2007.02.008zbMath1219.11082arXivmath/0604149OpenAlexW2055475331MaRDI QIDQ2474306

Tim Dokchitser, Vladimir Dokchitser

Publication date: 5 March 2008

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604149

zbMATH Keywords

elliptic curvesparity conjectureroot numbersSelmer rank

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05)

Related Items

Regulator constants and the parity conjecture ⋮ Selmer groups as flat cohomology groups ⋮ The \(p\)-parity conjecture for elliptic curves with a \(p\)-isogeny ⋮ The ℓ-parity conjecture over the constant quadratic extension ⋮ Computing Special Values of MotivicL-Functions ⋮ On the parity conjecture for abelian surfaces ⋮ Root numbers and parity phenomena ⋮ Iwasawa Theory, projective modules, and modular representations ⋮ Root numbers, Selmer groups, and non-commutative Iwasawa theory ⋮ Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction ⋮ Ranks of \(\mathrm{GL}_2\) Iwasawa modules of elliptic curves ⋮ Explicit isogeny descent on elliptic curves ⋮ On the Birch-Swinnerton-Dyer quotients modulo squares ⋮ Parity conjectures for elliptic curves over global fields of positive characteristic ⋮ Root numbers and parity of ranks of elliptic curves ⋮ On the parity of ranks of Selmer groups IV. With an appendix by Jean-Pierre Wintenberger ⋮ Local invariants of isogenous elliptic curves ⋮ The -parity conjecture for abelian varieties over function fields of characteristic

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