J. Belding, R. Bröker, A. Enge, and K. Lauter, Computing Hilbert Class Polynomials, Algorithmic Number Theory 8th International Symposium (ANTS VIII), pp.312-326, 2008.
DOI : 10.1007/978-3-540-79456-1_19
URL : https://hal.archives-ouvertes.fr/inria-00246115

C. Birkenhake and H. Lange, Complex abelian varieties, of Grundlehren der Mathematischen Wissenschaften, 2003.
DOI : 10.1007/978-3-662-06307-1

G. Bisson and A. V. Sutherland, Computing the endomorphism ring of an ordinary elliptic curve over a finite field, Journal of Number Theory, vol.131, issue.5, pp.815-831, 2011.
DOI : 10.1016/j.jnt.2009.11.003
URL : https://hal.archives-ouvertes.fr/inria-00383155

R. Bröker and K. Lauter, Modular Polynomials for Genus 2, LMS Journal of Computation and Mathematics, vol.7, issue.1, pp.326-339, 2009.
DOI : 10.2307/2007968

R. Bröker, A. V. Lauter, and . Sutherland, Modular polynomials via isogeny volcanoes, Mathematics of Computation, vol.81, issue.278, pp.1201-1231, 2012.
DOI : 10.1090/S0025-5718-2011-02508-1

R. Cosset, Applications des fonctions thêta à la cryptographie sur courbes hyperelliptiques, 2011.

P. Davis and P. Rabinowitz, Methods of Numerical Integration, 1984.

R. Dupont, Moyenne arithmético-géométrique, suites de Borchardt et applications, 2006.

K. Eisenträger and K. Lauter, A CRT algorithm for constructing genus 2 curves over finite fields, Arithmetic, Geometry and Coding Theory (AGCT-10), volume 21 of Séminaires et Congrès, pp.161-176, 2009.

N. Elkies, Elliptic and modular curves over finite fields and related computational issues, Computational perspectives on number theory: Proceedings of the conference in honor of A.O.L. Atkin, pp.21-76, 1998.

A. Enge, Computing modular polynomials in quasi-linear time, Mathematics of Computation, vol.78, issue.267, pp.1809-1824, 2009.
DOI : 10.1090/S0025-5718-09-02199-1
URL : https://hal.archives-ouvertes.fr/inria-00143084

]. A. Enge, Pari-gnump. http://www.multiprecision.org/index.php?prog= pari-gnump, 2014.

A. Enge, M. Gastineau, P. Théveny, and P. Zimmermann, Gnu mpc -a library for multiprecision complex arithmetic with exact rounding, 2012.

A. Enge and A. V. Sutherland, Class Invariants by the CRT Method, Algorithmic Number Theory 9th International Symposium (ANTS IX), pp.142-156, 2010.
DOI : 10.1007/978-3-642-14518-6_14
URL : https://hal.archives-ouvertes.fr/inria-00448729

A. Enge and E. Thomé, Computing Class Polynomials for Abelian Surfaces, Experimental Mathematics, vol.23, issue.2, 2014.
DOI : 10.1090/S0025-5718-2013-02712-3
URL : https://hal.archives-ouvertes.fr/hal-00823745

A. Enge and E. Thomé, Cmh -computation of Igusa class polynomials, 2014.

E. Freitag, Siegelsche Modulfunktionen, 1983.
DOI : 10.1007/978-3-642-68649-8

P. Gaudry, Algorithmique des courbes hyperelliptiques et applications à la cryptologie, 2000.
URL : https://hal.archives-ouvertes.fr/tel-00514848

E. Gottschling, Explizite Bestimmung der Randfl???chen des Fundamentalbereiches der Modulgruppe zweiten Grades, Mathematische Annalen, vol.83, issue.2, pp.103-124, 1959.
DOI : 10.1007/BF01342938

T. Granlund, Gmp -the GNU multiple precision arithmetic library, 2013.

D. Gruenewald, Explicit algorithms for Humbert surfaces, 2008.

G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann, GNU mpfr -a library for multiple-precision floating-point computations with exact rounding, 2012.

M. Hindry and J. H. Silverman, Diophantine geometry, volume 201 of Graduate text in mathematics, 2000.

F. Hirzebruch, G. Van, and . Geer, Lectures on Hilbert modular surfaces, volume 77 of Presses de l'université de Montréal, 1981.

J. I. Igusa, Arithmetic variety of moduli for genus 2, Annals of Mathematics, vol.72, issue.3, 1960.

J. I. Igusa, On Siegel modular forms of genus 2, 1962.

H. Klingen, Introductory lectures on Siegel modular forms, Cambridge Studies in Advanced Mathematics, vol.20, 1990.
DOI : 10.1017/CBO9780511619878

S. Lang, Elliptic functions, volume 112 of Graduate text in mathematics, 1987.

R. Manni, Modular Varieties with Level 2 Theta Structure, American Journal of Mathematics, vol.116, issue.6, pp.1489-1511, 1994.
DOI : 10.2307/2375056

J. Mestre, Construction de courbes de genre 2 ?? partir de leurs modules, Effective methods in algebraic geometry, pp.313-334
DOI : 10.1007/978-1-4612-0441-1_21

P. Molin, Intégration numérique et calculs de fonctions L, 2010.

D. Mumford, Abelian Varieties. Tata Institute of fundamental research studies in mathematics, 1970.

D. Mumford, Tata lectures on theta I, Progress in Mathematics. Birkhäuser, vol.28, 1983.

D. Mumford, Tata lectures on theta II, Progress in Mathematics. Birkhäuser, vol.43, 1984.
DOI : 10.1007/978-0-8176-4578-6

B. Runge, Endomorphism rings of abelian surfaces and projective models of their moduli spaces, Tohoku Mathematical Journal, vol.51, issue.3, pp.283-303, 1999.
DOI : 10.2748/tmj/1178224764

R. Schertz, Complex multiplication, volume 15 of New Mathematical Monographs, 2010.

L. Schläfli, Beweis der Hermiteschen Verwandlungstafeln für die elliptischen Modulfunktionen, Journal für die reine und angewandte Mathematik, pp.360-369, 1870.

R. Schoof, Counting points on elliptic curves over finite fields, Journal de Th??orie des Nombres de Bordeaux, vol.7, issue.1, pp.219-264, 1995.
DOI : 10.5802/jtnb.142

A. Schönhage and V. Strassen, Fast multiplication of large numbers, Computing, vol.150, issue.3-4, pp.281-292, 1971.
DOI : 10.1007/BF02242355

M. Streng, Complex multiplication of abelian surfaces, 2010.

A. V. Sutherland, Computing Hilbert class polynomials with the Chinese remainder theorem, Mathematics of Computation, vol.80, issue.273, pp.501-538, 2011.
DOI : 10.1090/S0025-5718-2010-02373-7

J. Thomae, Beitrag zur Bestimmung von ?(0, 0, . . . , 0) durch die Klassenmoduln algebraischer Funktionen, Journal für die Reine und Angewandte Mathematik, vol.70, pp.201-222, 1870.

J. Van-der-hoeven, Fast evaluation of holonomic functions, Theoretical Computer Science, vol.210, issue.1, pp.199-215, 1999.
DOI : 10.1016/S0304-3975(98)00102-9
URL : https://hal.archives-ouvertes.fr/hal-01374898

J. Zur-gathen and G. Jürgen, Modern Computer Algebra, 1999.
DOI : 10.1017/CBO9781139856065

H. Weber, Elliptische Funktionen und Algebraische Zahlen, 1908.

A. Weng, Constructing hyperelliptic curves of genus 2 suitable for cryptography, Mathematics of Computation, vol.72, issue.241, pp.435-458, 2003.
DOI : 10.1090/S0025-5718-02-01422-9