7-gons and genus three hyperelliptic curves

DOI10.1007/s13398-012-0079-1zbMath1293.11076OpenAlexW1975584730MaRDI QIDQ1940344

Hao Hao Wang, Jerome William Hoffman

Publication date: 6 March 2013

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-012-0079-1

zbMATH Keywords

abelian varietyreal multiplicationcurves of genus three

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Special algebraic curves and curves of low genus (14H45) Complex multiplication and moduli of abelian varieties (11G15)

Related Items (1)

Genus 3 curves whose Jacobians have endomorphisms by \(\mathbb{Q}(\zeta_7 + \overline{\zeta}_7)\)

Uses Software

• Magma
• Mathematica
• PARI/GP
• SageMath

Cites Work

• Elliptic fibrations of \(K3\) surfaces and QM Kummer surfaces
• On Cayley's explicit solution to Poncelet's porism
• The Magma algebra system. I: The user language
• Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two
• Endomorphism rings of abelian surfaces and projective models of their moduli spaces
• General form of Humbert's modular equation for curves with real multiplication of \(\Delta =5\)
• On Serre's reciprocity conjecture for 2-dimensional mod \(p\) representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\)
• On analytic families of polarized abelian varieties and automorphic functions
• Remarques sur un mémoire d'Hermite
• K3 Surfaces Associated with Curves of Genus Two
• Explicit Hyperelliptic Curves With Real Multiplication and Permutation Polynomials
• Mod 2 and mod 5 icosahedral representations
• Shimura Curve Computations Via K3 Surfaces of Néron–Severi Rank at Least 19
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