M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol.55, 1964.

A. R. Booker, J. Sijsling, A. V. Sutherland, J. Voight, and D. Yasaki, A database of genus-2 curves over the rational numbers, LMS Journal of Computation and Mathematics, vol.19, pp.235-254, 2016.

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.

J. Bost and J. Mestre, Moyenne arithmético-géométrique et périodes des courbes de genre 1 et 2, Gaz. Math, vol.1, issue.38, pp.36-64, 1988.

P. Richard, P. Brent, and . Zimmermann, Modern computer arithmetic, Cambridge Monographs on Applied and Computational Mathematics, vol.18, 2011.

M. M. Chawla and M. K. Jain, Error estimates for Gauss quadrature formulas for analytic functions, Math. Comp, vol.22, pp.82-90, 1968.

E. Costa, N. Mascot, J. Sijsling, and J. Voight, Rigorous computation of the endomorphism ring of a jacobian, 2017.

J. E. Cremona and T. Thongjunthug, The complex AGM, periods of elliptic curves over C and complex elliptic logarithms, J. Number Theory, vol.133, issue.8, pp.2813-2841, 2013.

B. Deconinck and . Mark-van-hoeij, Computing Riemann matrices of algebraic curves. Phys. D, 152, Advances in nonlinear mathematics and science, vol.153, pp.28-46, 2001.

J. Frauendiener and C. Klein, Computational approach to hyperelliptic riemann surfaces, Letters in Mathematical Physics, vol.105, issue.3, pp.379-400, 2015.

J. Frauendiener and C. Klein, Computational approach to compact Riemann surfaces, Nonlinearity, vol.30, issue.1, pp.138-172, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01446876

F. Johansson, Arb: a C library for ball arithmetic, ACM Communications in Computer Algebra, vol.47, issue.4, pp.166-169, 2013.

P. Kilicer, H. Labrande, R. Lercier, C. Ritzenthaler, J. Sijsling et al., Plane quartics over Q with complex multiplication, 2017.

J. K. and K. , On holomorphic differentials of some algebraic function field of one variable over c, Bulletin of the Australian Mathematical Society, vol.43, issue.3, pp.399-405, 1991.

, Greg Kuperberg. Kasteleyn cokernels. Electronic Journal of Combinatorics, vol.9, 2002.

H. Labrande, Explicit computation of the Abel-Jacobi map and its inverse. Theses, Université de Lorraine, 2016.
URL : https://hal.archives-ouvertes.fr/tel-01403849

, The LMFDB Collaboration. The L-functions and modular forms database, p.16, 2013.

N. Mascot, Computing modular Galois representations, Rend. Circ. Mat. Palermo, vol.62, issue.2, pp.451-476, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01110451

R. Miranda, Algebraic Curves and Riemann Surfaces, Graduate Studies in Mathematics, vol.5, 1995.

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

P. Molin and C. Neurohr, hcperiods: Arb and Magma packages for periods of superelliptic curves, 2017.

C. Towse, Weierstrass points on cyclic covers of the projective line, Transactions of the American Mathematical Society, vol.348, issue.8, pp.3355-3378, 1996.

C. L. Tretkoff and M. D. Tretkoff, Combinatorial group theory, riemann surfaces and differential equations, Contemporary Mathematics, vol.33, pp.467-517, 1984.

. Paul-van-wamelen, Equations for the jacobian of a hyperelliptic curve, Transactions of the American Mathematical Society, vol.350, issue.8, pp.3083-3106, 1998.

B. Paul and . Van-wamelen, Computing with the analytic Jacobian of a genus 2 curve, Discovering mathematics with Magma, vol.19, pp.117-135, 2006.