Curves of genus 2 with (n, n)--decomposable Jacobians
| dc.contributor.author | Shaska, Tony | |
| dc.date.accessioned | 2017-11-22T18:03:57Z | |
| dc.date.available | 2017-11-22T18:03:57Z | |
| dc.date.issued | 2001-05 | |
| dc.description.abstract | Let C be a curve of genus 2 and ψ1: C − → E 1 a map of degree n, from C to an elliptic curveE1 , both curves defined over C. This map induces a degree n map φ1:P1 − → P 1 which we call a Frey–Kani covering. We determine all possible ramifications for φ1. If ψ1:C − → E 1 is maximal then there exists a maximal map ψ2: C − → E 2 , of degree n, to some elliptic curveE2 such that there is an isogeny of degree n2from the JacobianJC to E1 × E2. We say thatJC is (n, n)-decomposable. If the degree n is odd the pair (ψ2, E2) is canonically determined. For n = 3, 5, and 7, we give arithmetic examples of curves whose Jacobians are (n, n)-decomposable. | en_US |
| dc.identifier.citation | Shaska, T. (2001). Curves of genus 2 with (N, N) decomposable Jacobians. Journal of Symbolic Computation, 31(5), 603-617. https://doi.org/10.1006/jsco.2001.0439 | en_US |
| dc.identifier.issn | 0747-7171, ESSN: 1095-855X | |
| dc.identifier.uri | http://hdl.handle.net/10323/4604 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Journal of Symbolic Computation | en_US |
| dc.subject | Genus two curves | en_US |
| dc.subject | Elliptic curves | en_US |
| dc.title | Curves of genus 2 with (n, n)--decomposable Jacobians | en_US |
| dc.type | Preprint | en_US |