X(11) and M 11

In this paper, we prove that the modular curve X(11) over a field of characteristic 3 admits the Mathieu group M 11 as an automorphism group. We also examine some aspects of the geometry of the curve X(11) in characteristic 3. In particular, we show that every point of the curve is a point of inflection, the curve has 110 hyperflexes and there are no inflectional triangles and 144 inflectional pentagons. The hyperflexes correspond to the supersingular elliptic curves. We comment on the relation Ward's quadrilinear invariant for M 12 to our work and announce for the first time the equations for Klein's A-curve of level 11.