On Elliptic Curves over Function Fields of Characteristic Two Original Research Article

Using Drinfeld modular curves we determine the places of supersingular reduction of elliptic curves over image2r(T) with certain conductors. This enables us to classify and describe explicitly all elliptic curves over image2r(T) having a conductor of degree 4. Our results also imply that extremal elliptic surfaces over the algebraic closure of image2 are unirational.