English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

An isogeny graph is a graph whose vertices are principally polarized abelianvarieties and whose edges are isogenies between these varieties. In his thesis,Kohel described the structure of isogeny graphs for elliptic curves and showedthat one may compute the endomorphism ring of an elliptic curve defined over afinite field by using a depth first search algorithm in the graph. In dimension2, the structure of isogeny graphs is less understood and existing algorithmsfor computing endomorphism rings are very expensive. Our setting considersgenus 2 jacobians with complex multiplication, with the assumptions that thereal multiplication subring is maximal and has class number one. We fullydescribe the isogeny graphs in that case. Over finite fields, we derive a depthfirst search algorithm for computing endomorphism rings locally at primenumbers, if the real multiplication is maximal. To the best of our knowledge,this is the first DFS-based algorithm in genus 2.

Isogeny graphs with maximal real multiplication