Constructing genus-3 hyperelliptic Jacobians with CM

DOI10.1112/S1461157016000322zbMath1404.11085arXiv1603.03832MaRDI QIDQ2971016

Christelle Vincent, Sorina Ionica, Jennifer S. Balakrishnan, Kristin E. Lauter

Publication date: 4 April 2017

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

Full work available at URL: https://arxiv.org/abs/1603.03832

Mathematics Subject Classification ID

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)] Theta functions and curves; Schottky problem (14H42)

Related Items (13)

Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication ⋮ On different expressions for invariants of hyperelliptic curves of genus 3 ⋮ 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 ⋮ Principally polarized squares of elliptic curves with field of moduli equal to \(\mathbb{Q}\) ⋮ An inverse Jacobian algorithm for Picard curves ⋮ Plane quartics over $\mathbb {Q}$ with complex multiplication ⋮ Primes Dividing Invariants of CM Picard Curves ⋮ genus3 ⋮ Modular invariants for genus 3 hyperelliptic curves ⋮ Super-isolated abelian varieties ⋮ Genus 3 hyperelliptic curves with CM via Shimura reciprocity ⋮ Spanning the isogeny class of a power of an elliptic curve

Uses Software

• SageMath

Cites Work

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• 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

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