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5-Torsion in the Shafarevich–Tate Group of a Family of Elliptic Curves

✍ Scribed by Cheryl DeLorme Beaver

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
192 KB
Volume
82
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 group.

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