A syringe includes a syringe body, which has a cylindrical portion and, adjoining the latter, a frustoconical portion, and a Luer lock connector, which has a Luer collar with an inner thread and a Luer cone with a through-channel. A bottom surface is formed between the Luer collar and Luer cone. The syringe body and the Luer lock connector are formed in one piece and are made of a cyclic olefin resin. The Luer collar has reinforcing ribs on its outer face.