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Journal Articles Experimental Mathematics Year : 2014

Computing class polynomials for abelian surfaces

Abstract

We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Dupont for evaluating ϑ- constants in quasi-linear time using Newton iterations on the Borchardt mean. We report on experiments with our implementation and present an example with class number 20016.
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Dates and versions

hal-00823745 , version 1 (17-05-2013)
hal-00823745 , version 2 (09-12-2013)

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Cite

Andreas Enge, Emmanuel Thomé. Computing class polynomials for abelian surfaces. Experimental Mathematics, 2014, 23 (2), pp.129-145. ⟨10.1080/10586458.2013.878675⟩. ⟨hal-00823745v2⟩
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