Bibliography with quick comments.

We list below articles, books, computations, relevant for our sub-topic. Some of these have appeared, some are available electronically on the web (WEB) , some are still in process (WORK-IN-PROG), and for some we have the teX-files (TEX). Also, some of these are directly related to our presentations, while others are background material

Directly related articles.

[A] Agashé, A.: On invisible elements of the Tate-Shafarevich group, Comptes Rendus de l’Académie des Sciences (France), to appear.

[A-K-M-M-M-P] (WORK-IN-PROG) An, S.Y., Kim S.Y., McCallum, W., Marshall, D., Marshall, S., Perlis, A.: On the Jacobian of a Curve of Genus One , in preparation.

[C-M] (WEB) (TEX) Cremona, J., Mazur, B.: Visualizing elements in the Shafarevich-Tate group, to appear in the Journal of Experimental Mathematics. [This article also can be downloaded as dvi or ps files from Cremona’s homepage: http://www.maths.ex.ac.uk/ cremona/papers/visual.dvi or http://www.maths.ex.ac.uk/ cremona/papers/visual.ps ]

[ M] (TEX) Mazur, B.: Visualizing elements of order three in the Shafarevich-Tate group, to appear in the Journal of Asian Mathematics.

[MSS] Merriman, J.R., Smart, N.P., and Siksek, S.: Explicit 4-descents on an elliptic curve, Acta Arithmetica LXXVII.4 (1996), pp. 385–404.

[O] O’Neil, C.: On the jacobians of curves of genus 1 in P^{1} ×P^{1} (WORK-IN-PROG) [Sa 1] Salmon, G.: A Treatise on the Higher Plane Curves (3rd edition), Hodges,

Foster and Figgis, Dublin 1879.

[Sa 2] Salmon, G.: A Treatise on the analytic geometry of three dimensions (7th edition), Chelsea, New York 1927.

[St] (WEB) Stein, W.: (A table of visible sha for higher-dimensional factors of the modular jacobian) http://math.berkeley.edu/ was/visible.html where you can view the document online.

[W] Weil, A.: Remarques sur un memoire d’Hermite, Arch. d. Math. 5 (1954) 197-202; reprinted in pp. 111-116 of volume II of André Weil Oeuvres Scientifiques Collected Papers Springer 1979

Background articles.

[Cr1] Cremona, J.: Algorithms for Modular Elliptic Curves (Second edition), Cambridge University Press, 1997.

[Cr 2] Cremona, J.: The Analytic order of � for Modular Elliptic Curves, Journal de Théorie des Nombres de Bordeaux 5 (1993), pp. 179–184.

[Cr 3] Cremona, J.: Computing the degree of the modular parametrization of a Modular Elliptic Curves, Mathematics of Computation 64 (1995), pp. 1235–1250.

[Cr4] (WEB) Cremona, J.: Modular elliptic curve data for conductors up to 5500,

available from ftp://euclid.ex.ac.uk/pub/cremona/data (see the readme file there).

[Cr5] (WEB) Cremona, J.: mwrank, a program for doing 2-descent on elliptic curves

over Q, available from ftp://euclid.ex.ac.uk/pub/cremona/progs (see the mwrank.readme

file there).

[R-S] Rubin, K., Silverberg, A.: Mod p representations of elliptic curves, pp. 148-161 in Elliptic curves, modular forms, and Fermat’s Last Theorem, International Press (1995)