On the variation of TateβShafarevich gro
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Mihran Papikian
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Article
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2005
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Elsevier Science
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English
β 368 KB
Let E be an elliptic curve over ] be an irreducible polynomial of odd degree, and let K =F ( β d). Assume (p) remains prime in K. We prove the analogue of the formula of Gross for the special value L(Eβ F K, 1). As a consequence, we obtain a formula for the order of the Tate-Shafarevich group I(E/K