[BCP97] Bosma, W., Cannon, J. and Playoust, C. The Magma algebra system. I. The user language. J. Symbolic Comput. 24 (3-4) (1997), 235–265. Computational algebra and number theory (London, 1993).

[BHPVdV04] Barth, W. P., Hulek, K., Peters, C. A. M. and Van de Ven, A. Compact complex surfaces volume 4 of Ergeb. Math. Grenzgeb. *3*. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. *3*rd Series. A Series of Modern Surveys in Mathematics]. (Springer-Verlag, Berlin, second edition, 2004).

[BT00] Bogomolov, F. A. and Tschinkel, Yu. Density of rational points on elliptic K3 surfaces. Asian J. Math. 4 (2) (2000), 351–368.

[Cha14] Charles, F. On the Picard number of K3 surfaces over number fields. Algebra Number Theory 8 (1) (2014), 1–17.

[CS99] Conway, J. H. and Sloane, N. J. A. Sphere packings, lattices and groups. Grundlehren Math Wiss vol. 290 [Fundamental Principles of Mathematical Sciences]. (Springer-Verlag, New York, third edition, 1999). With additional contributions by Bannai, E., Borcherds, R. E., Leech, J., Norton, S. P., Odlyzko, A. M., Parker, R. A., Queen, L. and Venkov, B. B.

[Dol96] Dolgachev, I. V. Mirror symmetry for lattice polarised K3 surfaces. J. Math. Sci. 81 (3) (1996), 2599–2630. Algebraic geometry, 4.

[EJ08] Elsenhans, A.-S. and Jahnel, J. *K*3 surfaces of Picard rank one and degree two. In Algorithmic number theory Lecture Notes in Comput. Sci. vol. 5011 (Springer, Berlin, 2008), pp. 212–225.

[EJ11] Elsenhans, A.-S. and Jahnel, J. The Picard group of a *K*3 surface and its reduction modulo *p*. Algebra Number Theory 5 (8) (2011), 1027–1040.

[Fes16] Festi, D. Topics in the arithmetic of del Pezzo and K3 surfaces. PhD. thesis. Universiteit Leiden (2016).

[Har77] Hartshorne, R. Algebraic geometry Graduate Texts in Math. No. 52. (Springer-Verlag, New York-Heidelberg, 1977).

[HKT13] Hassett, B., Kresch, A. and Tschinkel, Y. Effective computation of Picard groups and Brauer–Manin obstructions of degree two K3 surfaces over number fields. Rendiconti del Circolo Matematico di Palermo 62 (1) (2013), 137–151.

[HS00] Hindry, M. and Silverman, J. H. Diophantine geometry: an introduction Graduate Texts in Math. vol. 201 (Springer-Verlag, New York, 2000).

[Huy16] Huybrechts, D. Lectures on *K*3 surfaces Camb. Stud. Adv. Math. vol. 158 (Cambridge University Press, Cambridge, 2016).

[Ino78] Inose, H. Defining equations of singular *K*3 surfaces and a notion of isogeny. In *Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto*, 1977*)* (Kinokuniya Book Store, Tokyo, 1978), pp. 495–502.

[KT04] Kresch, A. and Tschinkel, Y. On the arithmetic of del Pezzo surfaces of degree 2. Proc. London Math. Soc. (3) 89 (3) (2004), 545–569.

[MP12] Maulik, D. and Poonen, B. Néron-Severi groups under specialisation. Duke Math. J. 161 (11) (2012), 2167–2206.

[Mum70] Mumford, D. Abelian varieties. Tata Institute of Fundamental Research Studies in Mathematics, No. 5. Published for the Tata Institute of Fundamental Research, Bombay (Oxford University Press, London, 1970).

[Nik80a] Nikulin, V. V. Integer symmetric bilinear forms and some of their geometric applications. Math USSR-Izv 14 (1) (1980), 103–167.

[Nik80b] Nikulin, V. V. Integral symmetric bilinear forms and some of their applications. Mathematics of the USSR-Izvestiya, 14 (1) (1980), 103.

[PTvL15] Poonen, B., Testa, D. and Luijk, R. van Computing Néron-Severi groups and cycle class groups. Compositio. Math. 151 (4) (2015), 713–734.

[SS10] Schütt, M. and Shioda, T. Elliptic surfaces. In Algebraic geometry in East Asia–-Seoul 2008 Adv. Stud. Pure Math. vol. 60 (Math. Soc. Japan, Tokyo, 2010), pp. 51–160.

[ST10] Stoll, M. and Testa, D. The surface parametrising cuboids. arXiv:1009.0388 (2010).

[VAV11] Várilly–Alvarado, A. and Viray, B. Failure of the Hasse principle for Enriques surfaces. Adv. Math. 226 (6) (2011), 4884–4901.

[vL07] van Luijk, R. An elliptic *K*3 surface associated to Heron triangles. J. Number Theory 123 (1) (2007), 92–119.