  Lame curves are a particular class of elliptic curves (with a torsion point
attached to them) which naturally arise when studying Lame operators with
finite monodromy. They can be realized as covers of the projective line
unramified outside three points and can be defined over number fields. This
paper investigates their p-adic properties. The main ingredient is formal/rigid
geometry and in particular the use of p-adic theta functions. As a consequence,
we can completely enumerate Lam\'e curves with bad reduction (by giving, among
the others, the p-adic valuation of their j-invariant) and describe the (local)
Galois action.
