An inverse Jacobian algorithm for Picard curves

DOI10.1007/s40993-021-00253-1zbMath1482.14035arXiv1611.02582OpenAlexW3153857912MaRDI QIDQ2028702

Christelle Vincent, Anna Somoza, Joan-Carles Lario

Publication date: 1 June 2021

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

Full work available at URL: https://arxiv.org/abs/1611.02582

zbMATH Keywords

hyperelliptic curvesexplicit algorithmgenus 3Picard curveinverse Jacobian

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Special algebraic curves and curves of low genus (14H45) Theta functions and abelian varieties (14K25) Complex multiplication and moduli of abelian varieties (11G15) Computational aspects of algebraic curves (14Q05) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items (1)

Spanning the isogeny class of a power of an elliptic curve

Uses Software

• SageMath
• GitHub
• genus3
• endomorphisms
• curve_reconstruction

Cites Work

• On the Torelli problem and Jacobian Nullwerte in genus three
• A generalization of Rosenhain's normal form for hyperelliptic curves with an application
• On the representation of the Picard modular function by \(\theta\) constants. I-II
• The hyperelliptic locus
• On products and algebraic families of Jacobian varieties
• Computing theta functions in quasi-linear time in genus two and above
• Constructing genus-3 hyperelliptic Jacobians with CM
• On a characterization of a Jacobian variety
• Examples of genus two CM curves defined over the rationals
• Determination of all imaginary abelian sextic number fields with class number ≤ 11
• Rigorous computation of the endomorphism ring of a Jacobian
• Construction of CM Picard curves
• Plane quartics over $\mathbb {Q}$ with complex multiplication
• Primes Dividing Invariants of CM Picard Curves
• Genus 3 hyperelliptic curves with CM via Shimura reciprocity
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
• Constructing Picard curves with complex multiplication using the Chinese remainder theorem
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