Geodesic
The Arithmetic of Genus Two Curves with (4,4)-Split Jacobians
Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 992-1024

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DOI

In this paper we study genus 2 curves whose Jacobians admit a polarized (4, 4)-isogeny to a product of elliptic curves. We consider base fields of characteristic different from 2 and 3, which we do not assume to be algebraically closed. We obtain a full classification of all principally polarized abelian surfaces that can arise from gluing two elliptic curves along their 4-torsion, and we derive the relation their absolute invariants satisfy.As an intermediate step, we give a general description of Richelot isogenies between Jacobians of genus 2 curves, where previously only Richelot isogenies with kernels that are pointwise defined over the base field were considered.Our main tool is a Galois theoretic characterization of genus 2 curves admitting multiple Richelot isogenies.
DOI : 10.4153/CJM-2011-039-3
Mots-clés : 11G30, 14H40, genus 2 curves, isogenies, split Jacobians, elliptic curves 
Bruin, Nils; Doerksen, Kevin. The Arithmetic of Genus Two Curves with (4,4)-Split Jacobians. Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 992-1024. doi: 10.4153/CJM-2011-039-3
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     title = {The {Arithmetic} of {Genus} {Two} {Curves} with {(4,4)-Split} {Jacobians}},
     journal = {Canadian journal of mathematics},
     pages = {992--1024},
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