An inverse of the modular invariant
  During the last few years of his life, Ramanujan had adamantly tried to invert the modular invariant. Subsequent efforts failed until May 30, 2011 when an explicit closed formula for an inverse was presented at the CCRAS (Moscow, Russia). This very formula, along with some special values of the modular invariant, is given in this paper. 
Semjon Adlaj
math.GM