The Tamagawa product method for predicting positive rank is subsumed by parity conjectures through an extension of Brauer relations to K-relations and a compatibility between Tamagawa numbers and local root numbers.
Brauer, Beziehungen zwischen Klassenzahlen von Teil korpern eines galoisschen K /dieresis.ts1orpers, Math
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Tamagawa numbers and positive rank of elliptic curves
The Tamagawa product method for predicting positive rank is subsumed by parity conjectures through an extension of Brauer relations to K-relations and a compatibility between Tamagawa numbers and local root numbers.