Reynald Lercier

R. Lercier and C. Ritzenthaler. G3Twists v1.1 : Reconstruction of genus 3 curves from their invariants. Developed with Magma (v.2.18), January 2013. [ tgz ]

This package provides tools to compute models of genus 3 curves and their geometric automorphism group from Shioda invariants. The algorithms used are described in [LR12]

J.-M. Couveignes, T. Ezome, and R. Lercier. GaloisTest v1.1 : a faster pseudo-primality test. Developed with Magma (v.2.18), May 2012. [ tgz ]

This script is an implementation of the pseudo-primality test described in [CEL12]

R. Lercier and C. Ritzenthaler. G2Twists v1.1 : Reconstruction of genus 2 curves from their invariants and twists over a finite field. Note that this package has been incorporated in the official magma distribution, since version 2.15, April 2009. [ tgz ]

This package provides tools to compute models of genus 2 curves and their geometric automorphism group from absolute invariants. Over a finite field, all the twists are computed too.

R. Lercier and J.-M. Couveignes. EllBasis v1.1 : Elliptic basis for finite fields. Developed with Magma (v.2.14), June 2008. [ tgz ]

This package provides MAGMA routines to handle basis for extensions (of degree d) of finite fields (with q elements) such that there exists fast algorithms to compute Frobenius and multiplications. These basis, available when there exists a point of order d on an elliptic curve defined over GF(q), are called elliptic (normal) basis in [CL08] and, at some extend, can be seen as a a generalisation of Gaussian Normal Basis.

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