Abstract
LetE be an elliptic curve defined overQ. By making some results of Rohrlich computationaly explicit, the root numberW is calculated as a product of local root numbers except whenE is ‘nonabelian’ at 2 or 3. The derivation of these explicit formulas depends in an essential way on the classification, carried out by the author in an earlier paper, of thoseE that become everywhere good or semi-stable in an abelian extension ofQ.
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Connell, I. Calculating root numbers of elliptic curves over Q. Manuscripta Math 82, 93–104 (1994). https://doi.org/10.1007/BF02567689
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DOI: https://doi.org/10.1007/BF02567689