Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Conjectural Rank Parities of Quartic and Sextic Twists of Elliptic
  Curves   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 $j$-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 previous results of Hadian and
Weidner on the behavior of $p$-Selmer ranks under $p$-twists.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol