Reductions of an elliptic curve and their Tate-Shafarevich groups
โ Scribed by A. C. Cojocaru; W. Duke
- Book ID
- 105872973
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 207 KB
- Volume
- 329
- Category
- Article
- ISSN
- 0025-5831
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let E be an elliptic curve over ] be an irreducible polynomial of odd degree, and let K =F ( โ d). Assume (p) remains prime in K. We prove the analogue of the formula of Gross for the special value L(Eโ F K, 1). As a consequence, we obtain a formula for the order of the Tate-Shafarevich group I(E/K
We compute the ,-Selmer group for a family of elliptic curves, where , is an isogeny of degree 5, then find a practical formula for the Cassels Tate pairing on the ,-Selmer groups and use it to show that a particular family of elliptic curves have non-trivial 5-torsion in their Shafarevich Tate grou