Flynn, E. V. Descent via isogeny in dimension 2. (English) Zbl 0835.14009 Acta Arith. 66, No. 1, 23-43 (1994). In Trans. Am. Math. Soc. 337, No. 2, 807-824 (1993; Zbl 0790.14028), D. M. Gordon and D. Grant described a complete 2-descent which applies to the Jacobian of curves of the form \(Y^2 = \prod^5_{i = 1} (X - a_i)\), where \(a_i \in \mathbb{Z}\). The paper under review discusses a technique (descent by 4-isogeny) applicable to curves of the form \(Y^2 = q_1 (X) q_2 (X)q_3 (X)\), where \(q_i (X)\) are quadratics over \(\mathbb{Z}\). The technique is illustrated by some examples where the ranks of the Jacobian are computed. Reviewer: J.R.Sendra (Madrid) Cited in 1 ReviewCited in 6 Documents MSC: 14H40 Jacobians, Prym varieties 14K02 Isogeny Keywords:2-descent; Jacobian of curves Citations:Zbl 0790.14028 PDFBibTeX XMLCite \textit{E. V. Flynn}, Acta Arith. 66, No. 1, 23--43 (1994; Zbl 0835.14009) Full Text: DOI EuDML