C. Birkenhake and H. Lange, Complex abelian varieties, vol.302, 2003.

G. Bisson, R. Cosset, and D. Robert, Magma package for explicit isogenies computation between abelian varieties, 2010.

W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system. I. The user language, Computational algebra and number theory, vol.24, pp.235-265, 1993.

A. Bostan, F. Morain, B. Salvy, and É. Schost, Fast algorithms for computing isogenies between elliptic curves, Math. Comp, vol.77, issue.263, pp.1755-1778, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00091441

L. Brambila-paz, S. B. Bradlow, O. Garca-prada, and S. Ramanan, Moduli Spaces and Vector Bundles, London Mathematical Society Lecture Note Series, vol.359, 2009.

L. Caporaso and E. Sernesi, Recovering plane curves from their bitangents, Journal of Algebraic Geometry, vol.12, issue.2, pp.225-244, 2003.

J. W. Cassels and E. V. Flynn, Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, Lecture Note Series, vol.230, 1996.

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

R. Cosset and D. Robert, Computing ( , )-isogenies in polynomial time on Jacobians of genus 2 curves, Mathematics of Computation, vol.84, pp.1953-1975, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00578991

J. Couveignes and T. Ezome, Computing functions on Jacobians and their quotients, LMS Journal of Computation and Mathematics, vol.18, pp.555-577, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01088933

C. Diem, On arithmetic and the discrete logarithm problem in class groups of curves, 2008.

I. Dolgachev and D. Lehavi, On isogenous principally polarized abelian surfaces, Curves and abelian varieties, vol.465, pp.51-69, 2008.

A. Fiorentino, Weber's formula for the bitangents of a smooth plane quartic, 2016.

P. Griffiths and J. Harris, Principles of algebraic geometry, 1978.

J. I. Igusa, Theta functions, volume 194 of Grundlehren der mathematischen Wissenschaften, 1972.

G. R. Kempf, Linear systems on abelian varieties, American Journal of Mathematics, vol.111, issue.1, pp.65-94, 1989.

S. Koizumi, Theta relations and projective normality of abelian varieties, American Journal of Mathematics, pp.865-889, 1976.

S. Lang, Abelian varieties, Interscience Tracts in Pure and Applied Mathematics, issue.7, 1959.

D. Lehavi, Any smooth plane quartic can be reconstructed from its bitangents, Israel Journal of Mathematics, vol.146, issue.1, pp.371-379, 2005.

D. Lehavi and C. Ritzenthaler, An explicit formula for the arithmetic-geometric mean in genus 3, Experiment. Math, vol.16, issue.4, pp.421-440, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01099887

D. Lubicz and D. Robert, Computing isogenies between Abelian Varieties, Compositio Mathematica, vol.148, issue.05, pp.1483-1515, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00446062

D. Lubicz and D. Robert, Computing separable isogenies in quasi-optimal time, LMS Journal of Computation and Mathematics, vol.18, pp.198-216, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00954895

D. Mumford, On the equations defining abelian varieties, I. Inventiones mathematicae, vol.1, issue.4, pp.287-354, 1966.

D. Mumford, On the equations defining abelian varieties, II. Inventiones mathematicae, vol.3, issue.2, pp.75-135, 1967.

D. Mumford, On the equations defining abelian varieties, III. Inventiones mathematicae, vol.3, issue.3, pp.215-244, 1967.

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

D. Mumford, Tata lectures on theta II, Progress in Mathematics. Birkhäuser Boston, vol.43, 1984.

J. S. Müller, Explicit Kummer varieties of hyperelliptic Jacobian threefolds, LMS Journal of Computation and Mathematics, vol.17, issue.1, pp.496-508, 2014.

S. Recillas, Jacobians of curves with g 1 4 's are the Prym's of trigonal curves, Bol. Soc. Mat. Mexicana, vol.19, issue.2, pp.9-13, 1974.

B. Riemann, Sur la théorie des fonctions abéliennes, 1898. Oeuvres de Riemann, p.487

C. Ritzenthaler, Point Counting on Genus 3 Non Hyperelliptic Curves, pp.379-394, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01099875

C. Ritzenthaler, Problèmes arithmétiques relatifs à certaines familles de courbes sur les corps finis, 2003.

D. Robert, Fonctions thêta et applications à la cryptographie, 2010.

B. Smith, Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves, vol.4965, pp.163-180, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00537860

B. Smith, Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method. Arithmeric, Geometry and Coding Theory -Contemporary mathematics, vol.574, pp.159-170, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00632118

M. Stoll, An explicit theory of heights for hyperelliptic Jacobians of genus three, 2017.

A. G. Stubbs, Hyperelliptic curves, 2000.

J. Vélu, Isogénies entre courbes elliptiques, Compte Rendu Académie Sciences Paris Série A-B, vol.273, pp.238-241, 1971.

H. Weber, Theorie der Abelschen Funktionen vom Geschlecht 3. Berlin : Druck und Verlag von Georg Reimer, p.1876

A. Weng, Konstruktion kryptographisch geeigneter Kurven mit komplexer Multiplikation, 2001.