×

Descent via isogeny in dimension 2. (English) Zbl 0835.14009

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.

MSC:

14H40 Jacobians, Prym varieties
14K02 Isogeny

Citations:

Zbl 0790.14028
PDFBibTeX XMLCite
Full Text: DOI EuDML