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In this paper we inspect from closer the local and global points of thetwists of the Klein quartic. For the local ones we use geometric arguments,while for the global ones we strongly use the modular interpretation of thetwists. The main result is providing families with (conjecturally infinitelymany) twists of the Klein quartic that at counter-examples to the Hasseprinciple.

Counter-examples to the Hasse principle among the twists of the Klein quartic