%
% Macro definitions for Book   Last changed 14/8/96
%
\documentstyle{amsppt}   % Needed if not preloaded
%
\magnification=\magstep 1

\vsize =  10.0 truein %\voffset -1.00 truein 
\hsize =   6.8 truein \hoffset -0.15 truein 

%
% Page numbers with wider spacing (openup 2pt)
%
%\newcount\chaponepages   \chaponepages   =   7
%\newcount\chaptwopages   \chaptwopages   =  51
%\newcount\appendixpages  \appendixpages  =  11
%\newcount\chapthreepages \chapthreepages =  49
%\newcount\chapfourpages  \chapfourpages  =   5
%\newcount\tabonepages    \tabonepages    = 146
%\newcount\tabtwopages    \tabtwopages    =   9
%\newcount\tabthreepages  \tabthreepages  =  49
%\newcount\tabfourpages   \tabfourpages   =  49
%\newcount\tabfivepages   \tabfivepages   =  12

%
% Page numbers with default spacing (no openup)
%
\newcount\chaponepages   \chaponepages   =   6
\newcount\chaptwopages   \chaptwopages   =  45
\newcount\appendixpages  \appendixpages  =  10
\newcount\chapthreepages \chapthreepages =  42
\newcount\chapfourpages  \chapfourpages  =   5
\newcount\tabonepages    \tabonepages    = 146
\newcount\tabtwopages    \tabtwopages    =   9
\newcount\tabthreepages  \tabthreepages  =  49
\newcount\tabfourpages   \tabfourpages   =  49
\newcount\tabfivepages   \tabfivepages   =  12


%\overfullrule 0pt
%
\Monograph
%
% Alterations to the style:
%
\catcode`\@=11
%
% (1) Fix to get rid of that logo on the first page:
%
%   \def\logo@{\baselineskip2pc}
\nologo
%
% (2) Don't like the indentation of \proclaims:
%
   \let\varindent@\noindent
%
%
% (3) References in normal size
%
   \let\refsfont@\tenpoint
%
\catcode`\@=\active
%
\define\Z{\Bbb Z}
\define\N{\Bbb N}
\define\Q{\Bbb Q}
\define\R{\Bbb R}
\define\C{\Bbb C}
\define\TT{\Bbb T}
\redefine\H{\hbox{$\Cal H$}}
\redefine\S{\hbox{$\Cal S$}}
\redefine\T{\hbox{$\Cal T$}}
\define\F{\hbox{$\Cal F$}}
\define\OO{\frak O} 
\define\SL{\hbox{\rm SL}}
\define\PSL{\hbox{\rm PSL}}
\define\GL{\hbox{\rm GL}}
\define\PGL{\hbox{\rm PGL}}
\define\knl{\hbox{\rm ker}}
\define\rk{\hbox{\rm rank}}
\define\tor{\text{tors}}
\define\disc{\text{disc}}
\define\ord{\hbox{\rm ord}}
\define\sgn{\hbox{\rm sign}}
\def\lcm{\hbox{\rm lcm}}
\def\agm{\hbox{\rm AGM}}
\def\Vol{\hbox{\rm Vol}}
\def\s{\sigma}
\def\t{\tau}
\def\w{\omega}
\define\eps{\varepsilon}
\define\BSD{Birch--Swin\-ner\-ton-Dyer}
\define\TS{Tate--Sha\-fa\-re\-vich}
\define\CM{complex multiplication}
\def\W{Weier\-strass}
\define\rp{\Omega_0}
\define\RP{\Omega}
\define\IP{\Omega_{\text{im}}}
\redefine\Re{\hbox{\rm Re}}
\redefine\Im{\hbox{\rm Im}}
\font\cyr=wncyr10
\define\Sha{\hbox{\cyr X}}
\def\G#1(#2){\Gamma_{#1}(#2)}
\define\mat(#1,#2;#3,#4){\pmatrix#1&#2\\#3&#4\endpmatrix}
\def\detmat#1#2#3#4{\left|\matrix#1&#2\\#3&#4\endmatrix\right|}
\redefine\div{\mid}
\define\ndiv{\nmid}
\define\<#1>{\left<#1\right>}
\def\slash#1{\left|#1\right.}
\def\fchi{f\otimes\chi}
\def\canht{\hat{h}}   % Canonical height
%
%  References
%
\newcount\refno  \refno=0
\def\newref#1{\advance\refno by1 \xdef#1{\the\refno}}
%
\newref\AtkinL
\newref\Antwerp   %ed. by Birch and Kuyk so ordered under B.!
\newref\BirchSD
\newref\BrumerK
\newref\BuhlerG
\newref\BuhlerGZ
\newref\Carayol
\newref\Cassels  %New book
\newref\Cohenbook % !!!NEW!!! 
\newref\Connell
\newref\Cox
\newref\JECa      % Compositio
\newref\JECb      % Compositio addendum
\newref\gammaone  % Gamma_1(N) paper
\newref\bsdiqf    % Joint paper with Elise
\newref\JCsha     % !!!NEW!!! 1993 paper on analytic order of Sha
\newref\JCdegphi  % !!!NEW!!! 1995 paper on computing deg(phi)
\newref\JCperiods % !!!NEW!!! 1996 paper on computing periods quickly
\newref\JCPS % !!!NEW!!! 1996 paper with Pascale
\newref\JCinvariants % !!!NEW!!! 1996 paper on invariants
\newref\Edixhoven % !!!NEW!!! 
\newref\Faltings
\newref\Ferm      % !!!NEW!!! High rank curves
\newref\Luiz      % !!!NEW!!! Luiz Figueiredo's thesis
\newref\GrossZagiera %Heegner points paper (early version)
\newref\GrossZagierb %Heegner points paper (full version)
%
%\newref\HaradaLang %% not referred to in 2nd edn.
%
\newref\Husemoller
\newref\Knapp     % !!!NEW!!! 
\newref\Kolyvagin
\newref\Kraus
\newref\Langa     % Elliptic functions book
\newref\Langb     % Modular forms book
\newref\Langc     % Elliptic curves: Diophantine analysis book
\newref\Laska
\newref\Laskabook 
%
%\newref\Livne  %% not referred to in 2nd edn.
%
\newref\Lutz
\newref\Manin
\newref\Mazur
\newref\MazurTa
\newref\MazurTb
\newref\MazurSD
\newref\Merel     % !!!NEW!!! 
\newref\Mestre
\newref\Murty
\newref\Nagao     % !!!NEW!!! Nagao's rank 21 curve
\newref\Nag
\newref\Neron
\newref\Pincha  % RGEP's thesis
\newref\Pinchb  % preprint, given a passing ref in Intro.
\newref\PZass   %Pohst and Zassenhaus' book
%
%\newref\Scholl %% not referred to in 2nd edn.
%
\newref\Schoof
\newref\PSthesis % !!!NEW!!! Pascale's thesis
\newref\Serre   %Isogeny paper
\newref\SerreNotes
\newref\Shimura
\newref\SSthesis % !!!NEW!!!  Samir's thesis
\newref\SSpaper  % !!!NEW!!!  Samir's paper
\newref\Silvera %Elliptic curves book I
\newref\Silverb %Computing heights paper
\newref\Silverc %Bounding  heights paper
\newref\Silverd %Elliptic curves book II           % !!!NEW!!! 
\newref\Silvere %2nd computing heights paper       % !!!NEW!!! 
\newref\Nigeletal % NPS+SS+JRM paper on 4-descents % !!!NEW!!! 
\newref\SDBirch
\newref\Tate     % Tate's algorithm in Antwerp IV
\newref\Tateht   % Tate's height paper
\newref\Tingley
\newref\Velu
\newref\Zagier
\newref\Zimmer % !!!NEW!!!
%
\def\und#1{{\it #1\/}}
\define\xtext#1{\noalign{\hbox{#1}}}
\def\part#1{\par\noindent{\rm(#1)\quad}}  % For parts of Theorems, etc.
%
\newcount\subsecno  \subsecno=0
\def\newsubsec#1{\advance\subsecno by1 
              \xdef#1{\chapno.\the\secno.\the\subsecno}
             }
%
\newcount\secno  \secno=0
\def\newsec#1{\advance\secno by1 
              \xdef#1{\chapno.\the\secno}
              \subsecno=0
             }
%
\newcount\eqno  \eqno=0
\def\neweq#1{\advance\eqno by1 
             \xdef#1{\sec.\the\eqno}
            }
%
\newcount\propno \propno=0
\def\newprop#1{\advance\propno by1 
               \xdef#1{\sec.\the\propno}
              }
%
\def\beginsection#1{\xdef\sec{#1}
                    \eqno=0
                    \propno=0
                    \subsecno=0
                   }
%
\def\beginsubsection#1{\xdef\subsec{#1}}
%
%
% DEFs FOR ALGORITHMS
%
\def\beginalg#1{\bigskip\goodbreak\hrule\medskip
                \leftline{\bf #1}
                \medskip\hrule\medskip\nobreak
                \tt    
               } 
\def\endalg{\par\nobreak\medskip\hrule\bigskip%\goodbreak
            \rm
           }
\def\D{$\Delta$} 
\newcount\lineno
\def\nline{\global\advance\lineno by1 %
           \tabalign\hfill\the\lineno.\quad& %
          }
\settabs 17\columns
\def\comm#1{\leftline{(\it #1)}}
\def\pow#1{$^{\text{\tt #1}}$}
\def\2{\pow2}
\def\3{\pow3}
\def\4{\pow4}
\def\5{\pow5}
\def\6{\pow6}
\def\DIV{$\mid$}
\def\NDIV{$\nmid$}
\def\={$\equiv$}
\def\NEQ{$\not=$}
\def\NEQUIV{$\not\equiv$}
%

\endinput
