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2002 Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups
Neil Dummigan
Experiment. Math. 11(4): 457-464 (2002).

Abstract

We consider the Bloch-Kato conjecture applied to the symmetric square L-function of an elliptic curve over $\QQ$, at $s=2$. In particular, we use a construction of elements of order l in a generalised Shafarevich-Tate group, which works when E has a rational point of infinite order and a rational point of order l. The existence of the latter places us in a situation where the recent theorem of Diamond, Flach, and Guo does not apply, but we find that the numerical evidence is quite convincing.

Citation

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Neil Dummigan. "Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups." Experiment. Math. 11 (4) 457 - 464, 2002.

Information

Published: 2002
First available in Project Euclid: 10 July 2003

zbMATH: 1162.11355
MathSciNet: MR1969637

Subjects:
Primary: 11G40, 14G10

Rights: Copyright © 2002 A K Peters, Ltd.

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Vol.11 • No. 4 • 2002
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