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Binary Quadratic Forms and Counterexamples to Hasse's Local-Global Principle
After a brief introduction to the classical theory of binary quadratic forms
we use these results for proving (most of) the claims made by P\'epin in a
series of articles on unsolvable quartic diophantine equations, and for
constructing families of counterexamples to the Hasse Principle for curves of
genus 1 defined by equations of the form