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- W3100499387 abstract "We study the behavior under twisting of the Selmer rank parities of a self-dual prime-degree isogeny on a principally polarized abelian variety defined over a number field, subject to compatibility relations between the twists and the isogeny. In particular, we study isogenies on abelian varieties whose Selmer rank parities are related to the rank parities of elliptic curves with [Formula: see text]-invariant 0 or 1728, assuming the Shafarevich–Tate conjecture. Using these results, we show how to classify the conjectural rank parities of all quartic or sextic twists of an elliptic curve defined over a number field, after a finite calculation. This generalizes the previous results of Hadian and Weidner on the behavior of [Formula: see text]-Selmer ranks under [Formula: see text]-twists." @default.
- W3100499387 created "2020-11-23" @default.
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- W3100499387 date "2019-10-01" @default.
- W3100499387 modified "2023-09-27" @default.
- W3100499387 title "On conjectural rank parities of quartic and sextic twists of elliptic curves" @default.
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- W3100499387 doi "https://doi.org/10.1142/s1793042119501057" @default.
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