[1]
Atiyah, M. F. and Wall, C. T. C., ‘Cohomology of groups’, inAlgebraic Number Theory (Proc. Instructional Conf., Brighton, 1965) (Thompson, Washington, DC, 1967), 94–115.

[2]
Baran, B., ‘An exceptional isomorphism between modular curves of level 13’, J. Number Theory
145 (2014), 273–300.

[3]
Baran, B., ‘An exceptional isomorphism between level 13 modular curves via Torelli’s theorem’, Math. Res. Lett.
21(5) (2014), 919–936.

[4]
Bhargava, M., Gross, B. H. and Wang, X., ‘Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits’, inRepresentations of Reductive Groups, (eds. Nevins, M. and Trapa, P. E.) Progress in Mathematics, 312 (Springer International Publishing, Boston, 2015), 139–171.

[5]
Bosch, S., Lütkebohmert, W. and Raynaud, M., Néron Models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) (Results in Mathematics and Related Areas (3)), 21 (Springer, Berlin, 1990).

[6]
Bruin, N. and Stoll, M., ‘Two-cover descent on hyperelliptic curves’, Math. Comp.
78(268) (2009), 2347–2370.

[7]
Deligne, P. and Mumford, D., ‘The irreducibility of the space of curves of given genus’, Publ. Math. Inst. Hautes Études Sci. (36) (1969), 75–109.

[8]
Demazure, M., ‘Résultant, discriminant’, Enseign. Math. (2)
58(3–4) (2012), 333–373.

[9]
Dixmier, J., ‘On the projective invariants of quartic plane curves’, Adv. Math.
64(3) (1987), 279–304.

[10]
Djabri, Z., Schaefer, E. F. and Smart, N. P., ‘Computing the *p*-Selmer group of an elliptic curve’, Trans. Amer. Math. Soc.
352(12) (2000), 5583–5597.

[11]
Flynn, E. V., Poonen, B. and Schaefer, E. F., ‘Cycles of quadratic polynomials and rational points on a genus-2 curve’, Duke Math. J.
90(3) (1997), 435–463.

[13]
Geissler, K. and Klüners, J., ‘Galois group computation for rational polynomials’, J. Symbolic Comput.
30(6) (2000), 653–674. Algorithmic methods in Galois theory.

[14]
Gelfand, I. M., Kapranov, M. M. and Zelevinsky, A. V., Discriminants, Resultants and Multidimensional Determinants, Modern Birkhäuser Classics (Birkhäuser Boston Inc., Boston, MA, 2008), reprint of the 1994 edition.

[15]
Gille, P. and Szamuely, T., Central Simple Algebras and Galois Cohomology, Cambridge Studies in Advanced Mathematics, 101 (Cambridge University Press, Cambridge, 2006).

[16]
Gross, B. H. and Harris, J., ‘On some geometric constructions related to theta characteristics’, inContributions to Automorphic Forms, Geometry, and Number Theory (Johns Hopkins University Press, Baltimore, MD, 2004), 279–311.

[17]
Hartshorne, R., Algebraic Geometry, Graduate Texts in Mathematics, 52 (Springer, New York, 1977).

[19]
Lang, S., Abelian Varieties (Springer, New York, 1983), reprint of the 1959 original.

[20]
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). Magma is available at http://magma.maths.usyd.edu.au/magma/.
[21]
McCallum, W. and Poonen, B., ‘The method of Chabauty and Coleman’, inExplicit Methods in Number Theory: Rational Points and Diophantine Equations, Panoramas et Synthèses, 36 (Société Mathématique de France, Paris, 2012), 99–117.

[22]
Milne, J. S., Arithmetic Duality Theorems, 2nd edn, (BookSurge, LLC, 2006).

[23]
Mordell, L. J., ‘On the rational solutions of the indeterminate equations of the third and fourth degrees’, Proc. Cambridge Phil. Soc.
21 (1922), 179–192.

[24]
Mumford, D., Abelian Varieties, Tata Institute of Fundamental Research Studies in Mathematics, 5 (Published for the Tata Institute of Fundamental Research, Bombay, 1970).

[25]
Mumford, D., ‘Theta characteristics of an algebraic curve’, Ann. Sci. Éc. Norm. Supèr. (4)
4 (1971), 181–192.

[26]
Mumford, David, Tata Lectures on Theta. II, Progress in Mathematics, 43 (Birkhäuser Boston Inc., Boston, MA, 1984), Jacobian theta functions and differential equations; with the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman and H. Umemura.

[27]
Pauli, S. and Roblot, X.-F., ‘On the computation of all extensions of a *p*-adic field of a given degree’, Math. Comp.
70(236) (2001), 1641–1659. (electronic).

[28]
Poonen, B., ‘Bertini theorems over finite fields’, Ann. of Math. (2)
160(3) (2004), 1099–1127.

[29]
Poonen, B. and Schaefer, E. F., ‘Explicit descent for Jacobians of cyclic covers of the projective line’, J. Reine Angew. Math.
488 (1997), 141–188.

[30]
Poonen, B., Schaefer, E. F. and Stoll, M., ‘Twists of *X* (7) and primitive solutions to *x*
^{2} + *y*
^{3} = *z*
^{7}
’, Duke Math. J.
137(1) (2007), 103–158.

[31]
Poonen, B. and Stoll, M., ‘The Cassels-Tate pairing on polarized abelian varieties’, Ann. of Math. (2)
150(3) (1999), 1109–1149.

[32]
Salmon, G., Lessons Introductory to the Modern Higher Algebra, 3rd edn, (Hodges, Foster, and Co., Dublin, 1876).

[33]
Salmon, G., A Treatise on the Higher Plane Curves, 3rd edn, (Hodges, Foster, and Figgis, Dublin, 1879).

[34]
Schaefer, E. F., ‘2-descent on the Jacobians of hyperelliptic curves’, J. Number Theory
51(2) (1995), 219–232.

[35]
Schaefer, E. F., ‘Class groups and Selmer groups’, J. Number Theory
56(1) (1996), 79–114.

[36]
Schaefer, E. F., ‘Computing a Selmer group of a Jacobian using functions on the curve’, Math. Ann.
310(3) (1998), 447–471.

[37]
Schaefer, E. F. and Stoll, M., ‘How to do a *p*-descent on an elliptic curve’, Trans. Amer. Math. Soc.
356(3) (2004), 1209–1231, (electronic).

[38]
Serre, J.-P., Local Fields, Graduate Texts in Mathematics, 67 (Springer, New York, 1979), translated from the French by Marvin Jay Greenberg.

[39]
Stauduhar, R. P., ‘The determination of Galois groups’, Math. Comp.
27 (1973), 981–996.

[40]
Stoll, M., ‘Independence of rational points on twists of a given curve’, Compos. Math.
142(5) (2006), 1201–1214.

[41]
Thorne, J. A., ‘The arithmetic of simple singularities’, PhD Thesis, Harvard University, April, 2012.

[42]
Weil, A., ‘L’arithmétique sur les courbes algébriques’, Acta Math.
52(1) (1929), 281–315.