Examples of CM curves of genus two defined over the reflex field

DOI10.1112/S1461157015000121zbMath1397.11103arXiv1307.0486OpenAlexW1869213401MaRDI QIDQ2942130

Marco Streng, Florian Bouyer

Publication date: 26 August 2015

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.0486

zbMATH Keywords

CM curvesIgusa class polynomialsreflex field

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Complex multiplication and moduli of abelian varieties (11G15) Complex multiplication and abelian varieties (14K22) Elliptic curves over local fields (11G07)

Related Items (8)

Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication ⋮ A reduction algorithm for Hilbert modular groups ⋮ The CM class number one problem for curves of genus 2 ⋮ A bound on the primes of bad reduction for CM curves of genus 3 ⋮ Rational points in the moduli space of genus two ⋮ Primes Dividing Invariants of CM Picard Curves ⋮ On the Colmez conjecture for non-abelian CM fields ⋮ Examples of abelian surfaces with everywhere good reduction

Uses Software

• PARI/GP
• SageMath
• CADO-NFS
• GMP-ECM
• RECIP

Cites Work

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• The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography
• Abelian varieties defined over their Fields of Moduli, I†

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