The CM class number one problem for curves of genus 2

DOI10.1007/s40993-022-00417-7OpenAlexW2262202050MaRDI QIDQ2679193

Pınar Kılıçer, Marco Streng

Publication date: 19 January 2023

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.04869

zbMATH Keywords

class numberCM fieldsabelian varietiesalgebraic curvesCM types

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) Complex multiplication and moduli of abelian varieties (11G15) Class numbers, class groups, discriminants (11R29) Complex multiplication and abelian varieties (14K22)

Related Items (1)

Modular invariants for genus 3 hyperelliptic curves

Uses Software

• SageMath
• Echidna
• RECIP
• curve_reconstruction

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Relative class numbers of normal CM-fields
• On the class number one problem for non-normal quartic CM-fields
• CM-fields with cyclic ideal class groups of 2-power orders
• On polarised class groups of orders in quartic CM-fields
• A complete determination of the complex quadratic fields of class-number one
• Imaginary Abelian number fields with class number one
• Diophantine analysis and modular forms
• Examples of CM curves of genus two defined over the reflex field
• Genus 2 Curves with Complex Multiplication
• Explicit Bounds for Primality Testing and Related Problems
• On Abelian Varieties with Complex Multiplication
• The Determination of all Imaginary, Quartic, Abelian Number Fields With Class Number 1
• Examples of genus two CM curves defined over the rationals
• Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one
• Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20
• Rigorous computation of the endomorphism ring of a Jacobian
• Correction : Abelian Varieties defined over their Fields of Moduli, I
• Explicit Lower bounds for residues at 𝑠=1 of Dedekind zeta functions and relative class numbers of CM-fields
• The field of moduli of abelian surfaces with complex multiplication.
• Advanced Topics in Computional Number Theory
• Plane quartics over $\mathbb {Q}$ with complex multiplication
• Primes Dividing Invariants of CM Picard Curves
• An arithmetic intersection formula for denominators of Igusa class polynomials
• Linear forms in the logarithms of algebraic numbers
• Abelian varieties defined over their Fields of Moduli, I†
• Principally polarized squares of elliptic curves with field of moduli equal to \(\mathbb{Q}\)

This page was built for publication: The CM class number one problem for curves of genus 2