We establish, for a substantial class of elliptic curves, that the arithmetic local constants introduced by Mazur and Rubin agree with quotients of analytic root numbers.
"Comparing local constants of ordinary elliptic curves in dihedral extensions." Funct. Approx. Comment. Math. 54 (2) 241 - 250, June 2016. https://doi.org/10.7169/facm/2016.54.2.7