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Conference Papers Year : 2010

Families of Explicit Isogenies of Hyperelliptic Jacobians

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Benjamin Smith
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Abstract

We construct three-dimensional families of hyperelliptic curves of genus 6, 12, and 14, two-dimensional families of hyperelliptic curves of genus 3, 6, 7, 10, 20, and 30, and one-dimensional families of hyperelliptic curves of genus 5, 10 and 15, all of which are equipped with an an explicit isogeny from their Jacobian to another hyperelliptic Jacobian. We show that the Jacobians are generically absolutely simple, and describe the kernels of the isogenies. The families are derived from Cassou--Noguès and Couveignes' explicit classification of pairs $(f,g)$ of polynomials such that $f(x_1) - g(x_2)$ is reducible.
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Dates and versions

inria-00420605 , version 1 (29-09-2009)

Identifiers

  • HAL Id : inria-00420605 , version 1
  • ARXIV : 0909.5406

Cite

Benjamin Smith. Families of Explicit Isogenies of Hyperelliptic Jacobians. Arithmetic, Geometry, Cryptography and Coding Theory 2009, Mar 2009, Luminy, France. pp.121-144. ⟨inria-00420605⟩
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