  In a well-known 1914 paper, Ramanujan gave a number of rapidly converging
series for $1/\pi$ which are derived using modular functions of higher level.
D. V. and G. V. Chudnovsky in their 1988 paper derived an analogous series
representing $1/\pi$ using the modular function $J$ of level 1, which results
in highly convergent series for $1/\pi$, often used in practice. In this paper,
we explain the Chudnovsky method in the context of elliptic curves, modular
curves, and the Picard-Fuchs differential equation. In doing so, we also
generalize their method to produce formulae which are valid around any singular
point of the Picard-Fuchs differential equation. Applying the method to the
family of elliptic curves parameterized by the absolute Klein invariant $J$ of
level 1, we determine all Chudnovsky-Ramanujan type formulae which are valid
around one of the three singular points: $0, 1, \infty$.
