Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups
Dummigan, Neil
Experiment. Math., Tome 11 (2002) no. 3, p. 457-464 / Harvested from Project Euclid
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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.
Publié le : 2002-05-14
Classification:  Elliptic curve,  symmetric square $L$-function,  Bloch-Kato conjecture,  11G40,  14G10 
@article{1057864655,
     author = {Dummigan, Neil},
     title = {Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups},
     journal = {Experiment. Math.},
     volume = {11},
     number = {3},
     year = {2002},
     pages = { 457-464},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1057864655}
}

Dummigan, Neil. Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups. Experiment. Math., Tome 11 (2002) no. 3, pp.  457-464. http://gdmltest.u-ga.fr/item/1057864655/