Geodesic
On the complexity of computing the 2-Selmer group of an elliptic curve
Glasgow mathematical journal, Tome 39 (1997) no. 3, pp. 251-257

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we give an algorithm for computing the 2-Selmer group of an elliptic curvewhich has complexity O(LD(0·5),c1)), where D is the absolute discriminant of the curve. Our algorithm is unconditional but the complexity estimate assumes the GRH and a standard conjecture on the distribution of smooth reduced ideals. This improves on the corresponding algorithm of Birch and Swinnerton-Dyer, which has complexity of O(√D). 
Siksek, S.; Smart, N. P. On the complexity of computing the 2-Selmer group of an elliptic curve. Glasgow mathematical journal, Tome 39 (1997) no. 3, pp. 251-257. doi: 10.1017/S0017089500032183
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