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The Tate-Shafarevich Group for Elliptic Curves with Complex Multiplication II

✍ Scribed by J. Coates; Z. Liang; R. Sujatha

Publisher
SP Birkhäuser Verlag Basel
Year
2010
Tongue
English
Weight
300 KB
Volume
78
Category
Article
ISSN
1424-9286

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📜 SIMILAR VOLUMES

On Elliptic Curves with Large Tate–Shafa
On Elliptic Curves with Large Tate–Shafarevich Groups
✍ Daisuke Atake 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 167 KB

Generalizing results of Lemmermeyer, we show that the 2-ranks of the Tate Shafarevich groups of quadratic twists of certain elliptic curves with a rational point of order 2 can be arbitrarily large. We use only quadratic residue symbols in a quadratic field to obtain our results.

On the variation of Tate–Shafarevich gro
On the variation of Tate–Shafarevich groups of elliptic curves over hyperelliptic curves
✍ Mihran Papikian 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 368 KB

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

5-Torsion in the Shafarevich–Tate Group
5-Torsion in the Shafarevich–Tate Group of a Family of Elliptic Curves
✍ Cheryl DeLorme Beaver 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 192 KB

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