## Average size of $2$-Selmer groups of elliptic curves, I

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- Trans. Amer. Math. Soc.
**358**(2006), 1563-1584 Request permission

## Abstract:

In this paper, we study a class of elliptic curves over $\mathbb {Q}$ with $\mathbb {Q}$-torsion group ${\mathbb {Z}}_{2}\times \mathbb {Z}_{2}$, and prove that the average order of the $2$-Selmer groups is bounded.## References

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## Additional Information

**Gang Yu**- Affiliation: Department of Mathematics, LeConte College, 1523 Greene Street, University of South Carolina, Columbia, South Carolina 29208
- Email: yu@math.sc.edu
- Received by editor(s): September 16, 2000
- Received by editor(s) in revised form: May 2, 2004
- Published electronically: October 31, 2005
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**358**(2006), 1563-1584 - MSC (2000): Primary 11G05, 14H52
- DOI: https://doi.org/10.1090/S0002-9947-05-03806-7
- MathSciNet review: 2186986