Computing isogenies between abelian varieties
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Publication:3167320
DOI10.1112/S0010437X12000243zbMath1259.14047arXiv1001.2016MaRDI QIDQ3167320
Publication date: 2 November 2012
Published in: Compositio Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1001.2016
Theta functions and abelian varieties (14K25) Isogeny (14K02) Effectivity, complexity and computational aspects of algebraic geometry (14Q20)
Related Items (16)
Arithmetic on abelian and Kummer varieties ⋮ Constructing all genus 2 curves with supersingular Jacobian ⋮ Computing functions on Jacobians and their quotients ⋮ A new proof of a Thomae-like formulafor non hyperelliptic genus 3 curves ⋮ Fast change of level and applications to isogenies ⋮ Cyclic Isogenies for Abelian Varieties with Real Multiplication ⋮ Isogeny graphs of ordinary abelian varieties ⋮ Computing separable isogenies in quasi-optimal time ⋮ Subexponential time relations in the class group of large degree number fields ⋮ Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with \((\ell ,\ell ,\ell)\)-isogenies ⋮ Computing isogenies between Jacobians of curves of genus 2 and 3 ⋮ Curves, Jacobians, and cryptography ⋮ Isogeny graphs with maximal real multiplication ⋮ Computing $(\ell ,\ell )$-isogenies in polynomial time on Jacobians of genus $2$ curves ⋮ Computing endomorphism rings of abelian varieties of dimension two ⋮ Spanning the isogeny class of a power of an elliptic curve
Cites Work
- Computing modular correspondences for abelian varieties
- The Weil pairing, and its efficient calculation
- Higher-dimensional 3-adic CM construction
- On the equations defining Abelian varieties. I-III
- Linear Systems on Abelian Varieties
- Equations for the Jacobian of a hyperelliptic curve
- Fast genus 2 arithmetic based on Theta functions
- The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography
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