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
✦ LIBER ✦
Vanishing of some cohomology groups and bounds for the Shafarevich–Tate groups of elliptic curves
✍ Scribed by Byungchul Cha
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 296 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0022-314X
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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