Christophe Ritzenthaler

Saiho-ji garden

Papers

Programs

Talks

Links

This is extracted from HAL. You can also find most of my documents directly on Arxiv.
Some packages in Magma which has been developed. They will be maintained and will eventually integrate the Magma official release. Please send comments and bugs to this email address. At the end of this section, you will find also some small programs or outputs related to articles. In my most recent articles, these data are directly stored on Arxiv as ancillary files.
Invariants and reconstruction of genus 2 hyperelliptic curves

This is a work in collaboration with R. Lercier. It has been implemented in Magma (v.2.13).

Magma Source
Invariants and reconstruction of genus 3 hyperelliptic curves

This is a work in collaboration with Reynald Lercier. It has been implemented in Magma (v.2.17).

Magma Source Paper
Fast computation of isomorphisms of hyperelliptic curves

This is a work in collaboration with Reynald Lercier and Jeroen Sijsling. It is now implemented in Magma 2.25-7.

Source Paper
Reconstructing plane quartics from their invariants

This is a work in collaboration with Reynald Lercier and Jeroen Sijsling. It is now implemented in Magma 2.25-7.

Source Paper
Decomposing Jacobians via Galois covers

This is a work in collaboration with Elisa Lorenzo García, Davide Lombardo and Jeroen Sijsling.

Source Paper
Spanning the isogeny class of the power of an elliptic curve

This is a work in collaboration with Markus Kirschmer, Fabien Narbonne and Damien Robert.

Source Paper
Functionalities for genus 2 and genus 3 curves

This is a work in collaboration with Reynald Lercier and Jeroen Sijsling. It has been implemented in Magma 2.25-7 and completes the work done before on genus 2 and 3.

Hyperelliptic Quartics Paper
  1. The Magma file to check the computation of the sign in Lemma 3.6 of A new proof of Thomae-like formula for non hyperelliptic genus 3 curves.
  2. The databases for p=11 and 13 (and the program to exploit them in Magma) and the statistics on the distributions of the trace for 7< p <59 of the article Parametrizing the moduli space of curves and application to smooth plane quartics over finite fields are contained in the following zip file.
  3. an implementation of an AGM algorithm for non-hyperelliptic curves of genus 3 has been worked out in collaboration with M. Fouquet and P. Gaudry. It has been implemented in Magma (v.2.09). This program does not work with the new version of MAGMA. You'll have to make changes in the definitions of the p-adic spaces.
  4. Here are several programs relative to the paper An explicit expression of Luroth invariant with Romain Basson, Reynald Lercier and Jeroen Sijsling. This Magma program provides a way to compute an expression of Luroth invariant and this is the final result. This Magma program generates random Luroth quartics of type L1 (with the notation of Ottaviani, Sernesi `On singular Luroth quartics') and this database contains 10,000 of them with rational coefficients. Finally this program checks that neither L1 nor L2 defines a new invariant. Note that they require the use of Echidna package available on this page.
  5. Magma programs to check the computations of Fast computation of isomorphisms of hyperelliptic curves and explicit descent with Reynald Lercier and Jeroen Sijsling: for Sections 1.5, 2.3.1 and 2.3.2: the programs, associated data and the package for genus 3 hyperelliptic curves; for Section 2.4; the general descent program, the resulting equation (8Mo) and the program to descend a particular example.
  6. Two programs related to On rationality of the intersection points of a line with a plane quartic with Roger Oyono: Computation of the correspondence curve in characteristic 2, Flexes in characteristic 3 (Maple 11).
  7. A program (collaboration with Philippe Trebuchet) in MAGMA which tests if a plane curve over a finite field is absolutely irreducible. It is based on E. Kaltofen article : Fast parallel absolute irreductibility testing, J. Symb. Comp. 1, (1985), 57-67.
  8. A program in MAGMA which computes the p-rank of the modular curves X(N).
  9. A basic program in MAGMA for computing the number of points on an elliptic curve with AGM as suggested by Jean-François Mestre.
Some slides of talks.
  1. Modular forms in small dimensions: geometry and arithmetic, Online Talk at Oberwolfach conference on moduli spaces and modular forms (Feb. 2021).
  2. Spanning the isogeny class of E^g, Online Talk at QNTAG seminar (May 2020).
  3. Modular forms in small dimensions, Talk in AGCT (June 2019).
  4. Smooth plane quartics with CM over Q, Talk in Barcelona (Feb. 2017).
  5. Reconstruction of smooth plane quartics from its invariants, Talk in Besançon (Apr. 2016).
  6. Distribution of traces of genus 3 curves over finite fields, Talk in Linz (Nov. 2013).
  7. Invariants and hyperelliptic curves: algorithmic aspects and open questions, Talk in Trento (Sep. 2012).
  8. Invariants and hyperelliptic curves: geometry, arithmetic and algorithmic aspects, Talk in Luminy (Oct. 2011).
  9. Algorithmic number theory and the allied theory of theta functions, Talk in Edinburgh (Oct. 2010).
  10. Rationality of intersection points of a line and a quartic, Talk in Istanbul (June 2010).
  11. Optimal curves of genus 1, 2 and 3, Talk in Leuven (May 2010).
  12. Completeness, Talk in Montréal (Apr. 2010).
  13. From the curve to its Jacobian and back, Talk in Montréal (Apr. 2010).
  14. Existence of dimension zero divisor, Talk at Antalya (Sept. 2009).
  15. Serre's obstruction for genus 3 curves, Talk in Guadeloupe (May 2009).
  16. Some old and new problems on genus 3 curve, Talk at ESF workshop (Mar. 2009).
  17. Quelles courbes elliptiques pour la cryptographie ? Talk at C2 (Mar. 2008).
  18. Addition law on a plane quartic, Talk in Tahiti (May 2007).
  19. AGM method for non hyperelliptic curves of genus 3, Talk in Bordeaux (Nov. 2003).
Website, working groups,etc.
  1. A database of curves with many points. It is a website in collaboration with E. Howe, K. Lauter and G. van der Geer and maintained by G. Oomens.
  2. The working group on effective theory of invariants.