Scott Arms, Álvaro Lozano-Robledo, and Steven J. Miller. Constructing one-parameter families of ellipticcurves with moderate rank. J. Number Theory, 123(2):388–402, 2007 

Manjul Bhargava, Daniel M. Kane, Hendrik W. Lenstra, Jr., Bjorn Poonen, and Eric Rains. Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. Camb. J. Math., 3(3):275–321, 2015. 

Dongho Byeon. Quadratic twists of elliptic curves associated to the simplest cubic fields. Proc. Japan Acad. Ser. A Math. Sci., 73(10):185–186, 1997. 

B. Conrad, K. Conrad, and H. Helfgott. Root numbers and ranks in positive characteristic. Adv. Math., 198(2):684–731, 2005. 

Ian Connell. Calculating root numbers of elliptic curves over Q. Manuscripta Math., 82(1):93–104, 1994. 

Tim Dokchitser and Vladimir Dokchitser. Elliptic curves with all quadratic twists of positive rank. Acta Arith., 137(2):193–197, 2009.
 
Julie Desjardins. Densité des points rationnels sur les surfaces elliptiques et les surfaces de del pezzo de degré 1. PhD thesis, Université Paris Diderot, Institut de mathematique de Jussieu Rive Gauche, available athttps://webusers.imj-prg.fr/~julie.desjardins/these.pdf, 2016. 

Julie Desjardins. On the variation of the root number in families of elliptic curves. Preprint, arXiv:math/1610.07440, 2016. 

Christophe Delaunay and Frédéric Jouhet. pℓ-torsion points in finite abelian groups and combinatorial identities. Adv. Math., 258:13–45, 2014. 

Sylvain Duquesne. Integral points on elliptic curves defined by simplest cubic fields. Experiment. Math., 10(1):91–102, 2001. 
David Farmer. Modeling families of l-functions. Preprint, arXiv:math/0511107v1, 2005. 

Emmanuel Halberstadt. Signes locaux des courbes elliptiques en 2 et 3. C. R. Acad. Sci. Paris Sér. I Math., 326(9):1047–1052, 1998.
 
Harald Helfgott. Root numbers and the parity problem. Preprint, arXiv:math/0305435, 2003. 

Harald Helfgott. On the square-free sieve. Acta Arith., 115(4):349–402, 2004. 

Harald Helfgott. On the behaviour of root numbers in families of elliptic curves. Preprint, arXiv:math/0408141v3, 2009. 

Zev Klagsbrun, Barry Mazur, and Karl Rubin. Disparity in Selmer ranks of quadratic twists of elliptic curves. Ann. of Math. (2), 178(1):287–320, 2013. 

Mayumi Kawachi and Shin Nakano. The 2-class groups of cubic fields and 2-descents on elliptic curves. Tohoku Math. J. (2), 44(4):557–565, 1992. 

Emmanuel Kowalski. Families of cusp forms. Publ. Math. Besançon Algèbre Théorie Nr., pages 5–40, 2013. 

Serge Lang. Algebraic number theory, volume 110 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1994. 

Rudolf Lidl and Harald Niederreiter. Finite fields, volume 20 of Encyclopedia of Mathematics and its Applications. Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. With a foreword by P. M. Cohn. 

Rick Miranda. An overview of algebraic surfaces. Notes for Lectures at the Summer School on Algebraic Geometry, Bilkent International Center for Advanced Studies, Bilkent University, Ankara, Turkey, 1995. 

Keiji Oguiso and Tetsuji Shioda. The Mordell-Weil lattice of a rational elliptic surface. Comment. Math. Univ. St. Paul., 40(1):83–99, 1991. 

Group PARI. PARI/GP, version 2.8.1. Bordeaux, 2016. 
Bjorn Poonen and Eric Rains. Random maximal isotropic subspaces and Selmer groups. J. Amer. Math. Soc., 25(1):245–269, 2012. 

Ottavio Rizzo. Average root numbers in families of elliptic curves. Proc. Amer. Math. Soc., 127(6):1597–1603, 1999. 

Ottavio G. Rizzo. Average root numbers for a nonconstant family of elliptic curves. Compositio Math., 136(1):1–23, 2003. 

David E. Rohrlich. Variation of the root number in families of elliptic curves. Compositio Math., 87(2):119–151, 1993. 

Fausto Romano. Sulla distribuzione della parità del rango di famiglie di curve ellittiche. Master thesis, supervised by Ottavio Rizzo, Corso di laurea di Matematica, Università degli Studi di Milan, 2005. 

Michael Rosen and Joseph H. Silverman. On the rank of an elliptic surface. Invent. Math., 133(1):43–67, 1998. 

Peter Sarnak. Definition of families of l-functions. letter to H. Iwaniec, P. Michel, A. Venkatesh and others, 2008. 

Charles F. Schwartz. On a family of elliptic surfaces with Mordell-Weil rank 4. Proc. Amer. Math. Soc., 102(1):1–8, 1988. 

Matthias Schütt and Tetsuji Shioda. Elliptic surfaces. Preprint, arXiv:math/0907.0298v3, 2010. 

Lawrence C. Washington. Class numbers of the simplest cubic fields. Math. Comp., 48(177):371–384, 1987.