49 citations · 143 across the 21 of their papers we have counts for
26 papers
Elliptic butterflies
Jean-Marc Couveignes, Reynald Lercier
We study natural evaluation and interpolation problems for elliptic functions and prove that they allow a recursive treatment using a variant of classical butterflies first introdu…
Reduction of Plane Quartics and Dixmier-Ohno invariants
Raymond van Bommel, Jordan Docking, Reynald Lercier +1
We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determini…
Reduction of Plane Quartics and Cayley Octads
Raymond van Bommel, Jordan Docking, Vladimir Dokchitser +2
We give a conjectural characterisation of the stable reduction of plane quartics over local fields in terms of their Cayley octads. This results in p-adic criteria that efficiently…
Functionality for isomorphism classes of curves and hypersurfaces
Thomas Bouchet, Reynald Lercier, Jeroen Sijsling +1
We describe algorithms based on invariant theory to solve problems on the geometry of curves, mainly those of genus 2, 3 and 4. New theoretical results building on the first author…
Fast computation of elliptic curve isogenies in characteristic two
Xavier Caruso, Elie Eid, Reynald Lercier
We propose an algorithm that calculates isogenies between elliptic curves defined over an extension of . It consists in efficiently solving with a logarithmic los…
Siegel modular forms of degree three and invariants of ternary quartics
Reynald Lercier, Christophe Ritzenthaler
We determine the structure of the graded ring of Siegel modular forms of degree 3. It is generated by 19 modular forms, among which we identify a homogeneous system of parameters w…