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Degree of irrationality of a product of two elliptic curves

. We consider the degree of irrationality d r ( S ) of some algebraic surface S . Firstly we give an estimate of d r ( S ) for a surface S with a structure of a (cid:12)ber space. Secondly we prove the existence of a nonsingular curve of genus 3 on E (cid:2) E for a certain elliptic curve E with complex multiplications. As a corollary, we obtain that d r ( E (cid:2) E ) = 3.