Visibility of Shafarevich-Tate Groups at Higher Level

by Dimitar Jetchev and William Stein


We study visibility of Shafarevich-Tate groups of modular abelian varieties in Jacobians of modular curves of higher level. We prove a theorem about the existence of visible elements at a specific higher level under hypotheses that can be verified explicitely. We also provide a table of examples of visible subgroups at higher level and state conjectures inspired by our data.

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