ECDL Project front page ...

Joseph H. Silverman Office: 214 Kassar House Phone: (401) 863-1132 Fax: (401) 863-9013 Email: jhs@math.brown.edu Email: joseph_silverman@brown.edu Mailing Address: Mathematics Department Box 1917 Brown University Providence, RI 02912 USA Teaching Schedule: Academic 2002/2003 Fall - Math 156 - Number Theory Research Interests: Number theory, elliptic curves, arithmetic and Diophantine geometry, ...

The Modular Forms Database William A. Stein Tables The Modular Forms Explorer Elliptic Curves Calculator Software Papers Lecture notes If you have any questions or comments, please send email to was@math.harvard.edu. In order to make these tables, I made extensive use of MAGMA, C++, LiDIA, and PARI, and greatly appreciate the work of the designers of these packages. If you find these tables ...

Table with ellitic curves with largest known ranks for curves with given torsion group ...

Information about various types of elliptic curves and associated theorems.

Detailed information about elliptic curves.

Bibliography for automorphic and modular forms, L-functions, and representation theory Last updated 1996 Also see the much newer specialized bibliography for Buildings, Classical Groups, and Representations of p-adic Groups The following biblography was compiled for my students. It is not at all exhaustive, and omits many recent papers. One might also see Jeff Adams' representation theory ...

R I C H A R D T A Y L O R Here are some recent papers. They are available either as dvi or as postscript files. They may be very slightly different from the published versions, e.g. they may not include corrections made to the proofs. Galois representations. (Review article.) R.Taylor preprint. dvi Postscript On the meromorphic continuation of degree two L-functions. R.Taylor preprint. dvi ...

Elliptic curves and formal groups by J. Lubin, J.-P. Serre and J. Tate This page contains scanned copies of the lecture notes of the seminar run by J. Lubin, J.-P. Serre and J. Tate, which is part of the Lecture notes prepared in connection with the seminars held at the Summer Institute on Algebraic Geometry, Whitney Estate, Woods Hole, Massachusetts, July 6-July 31, 1964 . Errata and ...

Software is like sex: it's better when it's free. -- Linus Torvalds Course Notes Full notes as dvi, pdf, and ps files for all the advanced course I taught between 1986 and 1999. Some of the notes give complete proofs (Group Theory, Fields and Galois Theory, Algebraic Number Theory, Class Field Theory, Algebraic Geometry), while others are more in the nature of introductory overviews to a topic.

TECC (Tiny Elliptic Curve Calculator) visitors since 12/1/1999. The current version of TECC is 2.4 (September 21, 2000). TECC Manual (html version) Version 2.2 Japanese Introduction This is a html version of the article submitted for the proceeding of the third Algebra and Computation conference held at Tokyo Metropolitan University. You can get TECC by ftp . Masanari Kida kida@sugaku.e-one.uec.

Rational Points on Elliptic Curves (last updated, Jul. 30, 2002) Curves (Short) Weierstrass forms Diophantine Equations y2 = x3 + b y2 = x3 + ax y2 = x3 + ax + b X3 + Y3 = A A : integer, X, Y : rational (y2 = x3 - 432A2) y2 = Dx4+1 Congruent numbers : D (y2 = x3 - D2x) Concordant numbers : n (y2 = x(x+1)(x+n) ) y2 = (x+p)(x2+p2) (x+y+z)(1/x+1/y+1/z)=n n, x, y, z : integer (y2 = x3 + (n2-6n-3)x2 ...

Detailed information about the concept of modular forms.

Tom's mathematical things As I said on the previous page, I'm a second-year post-graduate mathematician at the University of Nottingham, supervised by John Cremona, and working on computational number theory, concentrating on extending the well-known and effective algorithms for computing the ranks of elliptic curves over the rationals so that they might work over other number fields.. I've once ...

Information about elliptic curves, with links to related websites; in German.

Elliptic Divisibility Sequences Suppose u denotes the nth term of an integer divisibility sequence. This means all the terms are integers and u divides u whenever n divides m. The sequence is said to be an Elliptic Divisibility Sequence (hereafter EDS) if it satisfies the recurrence relation u u = u u u 2 - u u u 2 for all m n 0. In Morgan Ward's terminology, the sequence is proper if u =0, ...

I investigate the Birch and Swinnerton-Dyer conjecture, which ties together the constellation of invariants attached to an abelian variety. I attempt to verify this conjecture for certain specific modular abelian varieties of dimension greater than one. The key idea is to use Barry Mazur's notion of visibility, coupled with explicit computations, to produce lower bounds on the Shafarevich-Tate ...

MA 426 Elliptic curves This directory contains information for the course MA 426 on Elliptic curves, that I gave as a lecture course in 1999, 2000, as a reading course in 2001, and that is again on offer in 2002. The 45 page handout (5) contains the syllabus of the course, and indications for where to find the remaining material, almost all of which is covered in several textbooks. The student ...

Mathematics 574 Information Selected Topics in Number Theory Information concerning the course Mathematics 574 (Selected Topics in Number Theory) to be taught in Fall 2001 by J. Tunnell is kept here. The course will be an introduction to rational points on elliptic curves through examples of interesting elliptic curves. It will meet Monday and Wednesday 2:50-4:10 in Hill 425. The following ...

Modular Polynomials visitors since Sep. 18, 2000. This page links to the data of modular polynomials. There is also a Perl program mpoly.pl that generates a Maple program to use modular polynomial data. Now we have the data up to level 95 (4/1/2002). INSTRUCTION Download modular polynomial data of prime level in plain text format from Fujitsu Laboratory: http://www.labs.fujitsu.

Ken Ribet's Modular Forms Course Modular Forms and Hecke Operators These are the notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators. The version here is the original very rough form. Though they flow well, they contain all kinds of inaccuracies and are annoyingly incomplete. Thus at present I definitely wouldn't recommend them for study. Fortunately, I am ...

Tom Fisher's Home Page On 5 and 7 descents for elliptic curves Thomas Anthony Fisher, Clare College A dissertation submitted for the degree of Doctor of Philosphy at the University of Cambridge, August 2000 Abstract We perform descent calculations for the families of elliptic curves over Q with a rational point of order n = 5 or 7. These calculations give an estimate for the Mordell-Weil rank ...

Modular forms lecture notes William A. Stein William Stein Rochester: Charting the Land of Elliptic Curves (April 2002) Harvard: Charting the Land of Elliptic Curves (March 2002) Oberwolfach: Explicit Methods in Number Theory (July 2001) Some Modular Degree and Congruence Modulus Computations (Oberwolfach, July, 2001) The refined Eisenstein conjecture (William Stein, September, 1999) New ...

Hier eine kurze Beschreibung rein!

Best known conductors for elliptic curves of given rank The curves are given in the form . There are four classes of curves here, which I've colour-coded in what I hope is a meaningful way: Green Curve is known to have the smallest conductor for that rank, as a result of an exhaustive search over conductors Blue Curve is known to have the smallest conductor for that rank among curves with ...

Tables with currents records for generic ranks of elliptic curves with given torsion group ...

Research Page We will include here the postscript files for various papers and expository articles as they are completed. 1. Iwasawa Theory for Elliptic Curves. We study this subject by first proving that the p-primary subgroup of the classical Selmer group for an elliptic curve with good, ordinary reduction at a prime p has a very simple and elegant description which involves just the Galois ...

Tables of rank one Drinfeld modules Complete tables of sign-normalized, rank one, Drinfeld modules on the elliptic curves over finite fields of order less than 16 were computed by Dummit and Hayes (Mathematics of Computation, 62, 875-883) in 1994. These tables are available in two usable formats by anonymous ftp. The first format is designed for inclusion in TeX documents, and the second is ...

Prime Values of Elliptic Divisibility Sequences If u denotes the n-th term of an EDS then u grows very quickly. In fact log|u | ~ cn2. Chudnovsky and Chudnovsky considered some EDSs specified by writing down their first five terms and examined these sequences for prime terms. Since u is a divisibility sequence, which grows so quickly, it is sufficient to examine prime occurence of terms u with n ...

Home information media releases search site map membership and publications membership publications website accounts activities competitions grants math camps meetings - past meetings prizes & awards resources education employment research students women links other links other societies Henri Darmon - Recent progress in the theory of elliptic curves ...

Modular forms software William A. Stein Software: HECKE: Modular forms calculator A GP/PARI Hecke operators calculator Hijikata trace formula &nbsp Other People's: Verrill's fundamental domain drawer Peter Green's Heegner Points Package ...

Elliptic Curves II 4 hours of lectures per week. Content: The course is a continuation of the spring course: Elliptic curves over Q and C and will treat modular forms and elliptic curves. Prerequisites: Elliptic Curves, Chap. I-IV. Literature: Anthony W. Knapp: Elliptic Curves, Princeton University Press Jean-Pierre Serre: A Course in Arithmetic, GTM Springer Verlag Lars V. Ahlfors: Complex ...

Elliptic curves with CM defined over extensions of type (2, ..., 2) Joan-C. Lario This horizontal page contains data on the finite set (up to isomorphism) of elliptic curves with complex multiplication defined over extensions of type (2, ..., 2). An elliptic curve over the complex numbers is said to have CM if its algebra of endomorphisms is larger than the ring of rational integers. Class Field ...