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On the parametrization of solutions of quadratic equations. (Sur la paramétrisation des solutions des équations quadratiques.) (French) Zbl 1116.11024
Let \(Q(X,Y)\) be a binary integral quadratic form, then if \(Q=1\) has a solution it easily leads to an integral parametrization by quadratic forms \(q_i(s,t)\), \((i=1,2,3)\) such that \(Q(q_1(s,t),q_2(s,t))=q^2_3 (s,t)\). This also serves to make the class of \(Q\) the square of the class of \(q_3(s,t)\). As a consequence \(q_3\) is independent of the solution, and there are also applications to the 2-descent for elliptic curves [see the author, LMS J. Comput. Math. 5, 7–17 (2002; Zbl 1067.11015)]. The exposition also discusses the 2-class number and is remarkably self-contained.

11E16 General binary quadratic forms
Full Text: DOI Numdam EuDML
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