Geodesic
On local ``class fields'' of elliptic curves
Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 19-84

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In this paper a method is given for computing the Tate–Shafarevich pairing on elliptic curves for simple cyclic extensions. With this foundation the properties of the Tate–Shafarevich pairing are investigated over both a local field and a general local field of definition. 
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     author = {O. N. Vvedenskii},
     title = {On local ``class fields'' of elliptic curves},
     journal = {Izvestiya. Mathematics },
     pages = {19--84},
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     volume = {7},
     number = {1},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a1/}
}
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O. N. Vvedenskii. On local ``class fields'' of elliptic curves. Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 19-84. http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a1/