Calculation of Selmer groups of elliptic curves with rational 2-torsions and \(\theta\)-congruent number problem. (Q2783758)

The author gives an algorithm to compute the Selmer group associated to 2-isogeny for every elliptic curve over \(\mathbb{Q}\) having rational 2-torsion points. His result extends \textit{N. Aoki's} work [Comment. Math. Univ. St. Pauli 48, No. 1, 77--101 (1999; Zbl 0934.11030)] on the 2-Selmer groups of the elliptic curves related with a classical congruent number problem. The result is applied to solve a part of the \(\theta\)-congruent number problem, proposed by \textit{M. Fujiwara} in [Number Theory (K. Györy et al. (eds.)), Walter de Gruyter, Berlin, 235--241 (1998; Zbl 0920.11035)], which deals with triangles with rational sides and an angle \(\theta\).