Radical isogenies and modular curves

This article explores the connection between radical isogenies and modular curves. Radical are formulas designed for computation of chains fixed small degree $N$, introduced by Castryck, Decru, Vercauteren at Asiacrypt 2020. One significant advantage isogeny over other with a similar purpose is that they eliminate need to generate point order $N$ generates kernel isogeny. While were originally developed using elliptic curves in Tate normal form, Onuki Moriya have proposed degrees $3$ $4$ on Montgomery attempted obtain simpler form enhanced In this article, we translate original setup into language Additionally, solve an open problem regarding $X_0(N).$