Transformations of hypergeometric elliptic integrals

摘要: The paper classifies algebraic transformations of Gauss hypergeometric functions with the local exponent differences $(1/2,1/4,1/4)$, $(1/2,1/3,1/6)$ and $(1/3,1/3,1/3)$. These form a special class functions, arbitrary high degree. can be identified as elliptic integrals on genus 1 curves $y=x^3-x$ or $y=x^3-1$. Especially interesting are into themselves; these come from isogenies respective curves.