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On the variation of Tate–Shafarevich groups of elliptic curves over hyperelliptic curves

✍ Scribed by Mihran Papikian

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
368 KB
Volume
115
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let E be an elliptic curve over

] be an irreducible polynomial of odd degree, and let K =F ( √ d). Assume (p) remains prime in K. We prove the analogue of the formula of Gross for the special value L(E⊗ F K, 1). As a consequence, we obtain a formula for the order of the Tate-Shafarevich group I(E/K) when L(E⊗ F K, 1) = 0.

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