𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Shafarevich-Tate group of an elliptic curve

✍ Scribed by M. I. Bashmakov

Publisher
SP MAIK Nauka/Interperiodica
Year
1970
Tongue
English
Weight
307 KB
Volume
7
Category
Article
ISSN
0001-4346

No coin nor oath required. For personal study only.

📜 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

On invisible elements of the Tate-Shafar
On invisible elements of the Tate-Shafarevich group
✍ Amod Agashé 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 475 KB

Mazur [7] has introduced the concept of visible elements in the Tate-Shafarevich group of optimal modular elliptic curves. We generalized the notion to arbitrary abelian subvarieties of abelian varieties and found, based on calculations that assume the Birch-Swinnerton-Dyer conjecture, that there a