Genus 2 Curves with Complex Multiplication

DOI10.1093/imrn/rnr052zbMath1236.14033arXiv1003.4759OpenAlexW2963918361MaRDI QIDQ3224207

Eyal Z. Goren, Kristin E. Lauter

Publication date: 29 March 2012

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.4759

zbMATH Keywords

Genus 2 curvesComplex multiplicationAbelian surfaces

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) Jacobians, Prym varieties (14H40) Complex multiplication and moduli of abelian varieties (11G15)

Related Items (13)

Arithmetic on abelian and Kummer varieties ⋮ Real-dihedral harmonic Maass forms and CM-values of Hilbert modular functions ⋮ Examples of CM curves of genus two defined over the reflex field ⋮ The CM class number one problem for curves of genus 2 ⋮ A universal genus-two curve from Siegel modular forms ⋮ A bound on the primes of bad reduction for CM curves of genus 3 ⋮ Constructing Picard curves with complex multiplication using the Chinese remainder theorem ⋮ Difference of modular functions and their CM value factorization ⋮ Tropical geometry of genus two curves ⋮ Primes Dividing Invariants of CM Picard Curves ⋮ Computing the 2-adic canonical lift of genus 2 curves ⋮ Computing Igusa class polynomials ⋮ Constructing abelian surfaces for cryptography via Rosenhain invariants

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