  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 of algebraic transformations of
Gauss hypergeometric functions, of arbitrary high degree. The Gauss
hypergeometric functions can be identified as elliptic integrals on the genus 1
curves $y=x^3-x$ or $y=x^3-1$. Especially interesting are algebraic
transformations of the hypergeometric functions into themselves; these
transformations come from isogenies of the respective elliptic curves.
