A note on the Tate pairing of curves over finite fields
β Scribed by F. Hess
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 76 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0003-889X
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## Abstract In this paper we study the Newton polygon of the __L__ βpolynomial __L__ (__t__) associate to the Picard curves __y__^3^ = __x__^4^ β 1,β__y__^3^ = __x__^4^ β __x__ defined over a finite field π½~__p__~ . In the former case we get a complete classification. In the latter case we obtai
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