Genus-2 curves and Jacobians with a given number of points

DOI10.1112/S1461157014000461zbMath1387.14086arXiv1403.6911MaRDI QIDQ5173201

Peter Stevenhagen, Reinier Bröker, Everett W. Howe, Kristin E. Lauter

Publication date: 9 February 2015

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

Full work available at URL: https://arxiv.org/abs/1403.6911

zbMATH Keywords

Jacobiancurvesgenus

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) Jacobians, Prym varieties (14H40) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Complex multiplication and moduli of abelian varieties (11G15) Complex multiplication and abelian varieties (14K22)

Related Items (12)

Multiradical isogenies ⋮ From hyperelliptic to superelliptic curves ⋮ Optimal Encodings to Elliptic Curves of \(\boldsymbol{j}\)-Invariants 0, 1728 ⋮ On families of 9-congruent elliptic curves ⋮ Curves of medium genus with many points ⋮ Decomposing Jacobians Via Galois covers ⋮ The automorphism group of the non-split Cartan modular curve of level 11 ⋮ A direct key recovery attack on SIDH ⋮ A universal genus-two curve from Siegel modular forms ⋮ Efficient computation of \((3^n,3^n)\)-isogenies ⋮ On 12-congruences of elliptic curves ⋮ Curves, Jacobians, and cryptography

Cites Work

• Unnamed Item
• Jacobians in isogeny classes of abelian surfaces over finite fields
• The Difference Between Consecutive Primes, II
• Computing Igusa class polynomials
• Efficient CM-constructions of elliptic curves over finite fields
• Genus 2 fields with degree 3 elliptic subfields
• Large torsion subgroups of split Jacobians of curves of genus two or three
• Accelerating the CM method
• LARGE DIFFERENCES BETWEEN CONSECUTIVE PRIMES
• Lower bounds for relative class numbers of imaginary abelian number fields and CM-fields

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