This is e-TeX, Version 3.14159-2.1 (Web2C 7.4.5) (format=latex 2004.8.22) 25 AUG 2004 14:19 entering extended mode **\nonstopmode\input bsd01.tex (./bsd01.tex (./mcom-l.cls Document Class: mcom-l 1996/02/02 v1.2f MCOM Author Class (/usr/share/texmf/tex/latex/amscls/amsart.cls Document Class: amsart 2000/10/26 v2.08 \linespacing=\dimen102 \normalparindent=\dimen103 \normaltopskip=\skip41 (/usr/share/texmf/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/07/18 v2.13 AMS math features \@mathmargin=\skip42 For additional information on amsmath, use the `?' option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty Package: amstext 2000/06/29 v2.01 (/usr/share/texmf/tex/latex/amsmath/amsgen.sty File: amsgen.sty 1999/11/30 v2.0 \@emptytoks=\toks14 \ex@=\dimen104 )) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty Package: amsbsy 1999/11/29 v1.2d \pmbraise@=\dimen105 ) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty Package: amsopn 1999/12/14 v2.01 operator names ) \inf@bad=\count79 LaTeX Info: Redefining \frac on input line 211. \uproot@=\count80 \leftroot@=\count81 LaTeX Info: Redefining \overline on input line 307. \classnum@=\count82 \DOTSCASE@=\count83 LaTeX Info: Redefining \ldots on input line 379. LaTeX Info: Redefining \dots on input line 382. LaTeX Info: Redefining \cdots on input line 467. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen106 LaTeX Font Info: Redeclaring font encoding OML on input line 567. LaTeX Font Info: Redeclaring font encoding OMS on input line 568. \macc@depth=\count84 \c@MaxMatrixCols=\count85 \dotsspace@=\muskip10 \c@parentequation=\count86 \dspbrk@lvl=\count87 \tag@help=\toks15 \row@=\count88 \column@=\count89 \maxfields@=\count90 \andhelp@=\toks16 \eqnshift@=\dimen107 \alignsep@=\dimen108 \tagshift@=\dimen109 \tagwidth@=\dimen110 \totwidth@=\dimen111 \lineht@=\dimen112 \@envbody=\toks17 \multlinegap=\skip43 \multlinetaggap=\skip44 \mathdisplay@stack=\toks18 LaTeX Info: Redefining \[ on input line 2666. LaTeX Info: Redefining \] on input line 2667. ) LaTeX Font Info: Try loading font information for U+msa on input line 395. (/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 2001/10/25 v2.2f \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 132. ) \copyins=\insert233 \abstractbox=\box28 \listisep=\skip45 \c@part=\count91 \c@section=\count92 \c@subsection=\count93 \c@subsubsection=\count94 \c@paragraph=\count95 \c@subparagraph=\count96 \c@figure=\count97 \c@table=\count98 \abovecaptionskip=\skip46 \belowcaptionskip=\skip47 \captionindent=\dimen113 \thm@style=\toks19 \thm@bodyfont=\toks20 \thm@headfont=\toks21 \thm@notefont=\toks22 \thm@headpunct=\toks23 \thm@preskip=\skip48 \thm@postskip=\skip49 \thm@headsep=\skip50 \dth@everypar=\toks24 )) (./srcltx.sty Package: srcltx 1999/10/11 v1.002 DVI Search \PAGETOP=\count99 \LASTLINE=\count100 \INPSP=\count101 \everypar=\toks25 ) (/usr/share/texmf/tex/generic/xypic/xy.sty (/usr/share/texmf/tex/generic/xypic/xy.tex Bootstrap'ing: catcodes, docmode, (/usr/share/texmf/tex/generic/xypic/xyrecat.tex) (/usr/share/texmf/tex/generic/xypic/xyidioms.tex) Xy-pic version 3.7 <1999/02/16> Copyright (c) 1991-1998 by Kristoffer H. Rose Xy-pic is free software: see the User's Guide for details. Loading kernel: messages; fonts; allocations: state, \X@c=\dimen114 \Y@c=\dimen115 \U@c=\dimen116 \D@c=\dimen117 \L@c=\dimen118 \R@c=\dimen119 \Edge@c=\toks26 \X@p=\dimen120 \Y@p=\dimen121 \U@p=\dimen122 \D@p=\dimen123 \L@p=\dimen124 \R@p=\dimen125 \Edge@p=\toks27 \X@origin=\dimen126 \Y@origin=\dimen127 \X@xbase=\dimen128 \Y@xbase=\dimen129 \X@ybase=\dimen130 \Y@ybase=\dimen131 \X@min=\dimen132 \Y@min=\dimen133 \X@max=\dimen134 \Y@max=\dimen135 \lastobjectbox@=\box29 \zerodotbox@=\box30 \almostz@=\dimen136 direction, \d@X=\dimen137 \d@Y=\dimen138 \K@=\count102 \KK@=\count103 \Direction=\count104 \K@dXdY=\dimen139 \K@dYdX=\dimen140 \xyread@=\read1 \xywrite@=\write3 \csp@=\count105 \quotPTK@=\dimen141 utility macros; pictures: \xy, positions, \swaptoks@@=\toks28 \connectobjectbox@@=\box31 objects, \styletoks@=\toks29 decorations; kernel objects: directionals, circles, text; options; algorithms: directions, edges, connections; Xy-pic loaded) Package: xy 1999/02/16 Xy-pic version 3.7 (/usr/share/texmf/tex/generic/xypic/xyall.tex Xy-pic option: All features v.3.3 (/usr/share/texmf/tex/generic/xypic/xycurve.tex Xy-pic option: Curve and Spline extension v.3.7 curve, \crv@cnt@=\count106 \crvpts@=\toks30 \splinebox@=\box32 \splineval@=\dimen142 \splinedepth@=\dimen143 \splinetol@=\dimen144 \splinelength@=\dimen145 circles, \L@=\dimen146 loaded) (/usr/share/texmf/tex/generic/xypic/xyframe.tex Xy-pic option: Frame and Bracket extension v.3.7 loaded) (/usr/share/texmf/tex/generic/xypic/xycmtip.tex Xy-pic option: Computer Modern tip extension v.3.3 (/usr/share/texmf/tex/generic/xypic/xytips.tex Xy-pic option: More Tips extension v.3.3 loaded) loaded) (/usr/share/texmf/tex/generic/xypic/xyline.tex Xy-pic option: Line styles extension v.3.6 \xylinethick@=\dimen147 loaded) (/usr/share/texmf/tex/generic/xypic/xyrotate.tex Xy-pic option: Rotate and Scale extension v.3.3 loaded) (/usr/share/texmf/tex/generic/xypic/xycolor.tex Xy-pic option: Colour extension v.3.3 loaded) (/usr/share/texmf/tex/generic/xypic/xymatrix.tex Xy-pic option: Matrix feature v.3.4 \Row=\count107 \Col=\count108 \queue@=\toks31 \queue@@=\toks32 \qcount@=\count109 \qcount@@=\count110 \matrixsize@=\count111 loaded) (/usr/share/texmf/tex/generic/xypic/xyarrow.tex Xy-pic option: Arrow and Path feature v.3.5 path, \ar, loaded) (/usr/share/texmf/tex/generic/xypic/xygraph.tex Xy-pic option: Graph feature v.3.7 loaded) loaded)) :<+ macros.tex \@input{macros.aux} \openout2 = `macros.aux'. (./macros.tex (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty Package: amssymb 2002/01/22 v2.2d ) \c@theorem=\count112 \c@listnum=\count113 (/usr/share/texmf/tex/latex/hyperref/hyperref.sty Package: hyperref 2003/01/22 v6.73n Hypertext links for LaTeX (/usr/share/texmf/tex/latex/graphics/keyval.sty Package: keyval 1999/03/16 v1.13 key=value parser (DPC) \KV@toks@=\toks33 ) \@linkdim=\dimen148 \Hy@linkcounter=\count114 \Hy@pagecounter=\count115 (/usr/share/texmf/tex/latex/hyperref/pd1enc.def File: pd1enc.def 2003/01/22 v6.73n Hyperref: PDFDocEncoding definition (HO) ) (/usr/share/texmf/tex/latex/config/hyperref.cfg File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive and teTeX ) Package hyperref Info: Hyper figures OFF on input line 1792. Package hyperref Info: Link nesting OFF on input line 1797. Package hyperref Info: Hyper index ON on input line 1800. Package hyperref Info: Plain pages ON on input line 1805. Package hyperref Info: Backreferencing OFF on input line 1812. Implicit mode ON; LaTeX internals redefined Package hyperref Info: Bookmarks ON on input line 1916. (/usr/share/texmf/tex/latex/misc/url.sty \Urlmuskip=\muskip11 Package: url 1999/03/28 ver 1.5x Verb mode for urls, etc. ) LaTeX Info: Redefining \url on input line 2055. \Fld@menulength=\count116 \Field@Width=\dimen149 \Fld@charsize=\dimen150 \Choice@toks=\toks34 \Field@toks=\toks35 Package hyperref Info: Hyper figures OFF on input line 2513. Package hyperref Info: Link nesting OFF on input line 2518. Package hyperref Info: Hyper index ON on input line 2521. Package hyperref Info: backreferencing OFF on input line 2528. Package hyperref Info: Link coloring OFF on input line 2533. \c@Item=\count117 \c@Hfootnote=\count118 ) *hyperref using driver hypertex* (/usr/share/texmf/tex/latex/hyperref/hypertex.def File: hypertex.def 2003/01/22 v6.73n Hyperref driver for HyperTeX specials )) :<- (./bsd01.aux) \openout1 = `bsd01.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 19. LaTeX Font Info: ... okay on input line 19. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 19. LaTeX Font Info: ... okay on input line 19. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 19. LaTeX Font Info: ... okay on input line 19. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 19. LaTeX Font Info: ... okay on input line 19. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 19. LaTeX Font Info: ... okay on input line 19. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 19. LaTeX Font Info: ... okay on input line 19. LaTeX Font Info: Checking defaults for OT2/cmr/m/n on input line 19. LaTeX Font Info: Try loading font information for OT2+cmr on input line 19. (/usr/share/texmf/tex/latex/cyrillic/ot2cmr.fd File: ot2cmr.fd 2001/08/11 v3.2c Computer Modern Cyrillic font definitions ) LaTeX Font Info: ... okay on input line 19. LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 19. LaTeX Font Info: ... okay on input line 19. LaTeX Font Info: Try loading font information for U+msa on input line 19. (/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 19. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) Package hyperref Info: Link coloring OFF on input line 19. (/usr/share/texmf/tex/latex/hyperref/nameref.sty Package: nameref 2001/01/27 v2.19 Cross-referencing by name of section \c@section@level=\count119 ) LaTeX Info: Redefining \ref on input line 19. LaTeX Info: Redefining \pageref on input line 19. LaTeX Font Info: Try loading font information for OMS+cmr on input line 21. (/usr/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <6> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 21. (./bsd01.toc LaTeX Font Info: Try loading font information for OT2+wncyr on input line 8. (/usr/share/texmf/tex/latex/cyrillic/ot2wncyr.fd File: ot2wncyr.fd 1999/12/17 v3.2a Computer Modern Cyrillic font definitions )) \tf@toc=\write4 \openout4 = `bsd01.toc'. [1 ] Overfull \hbox (1.38979pt too wide) in paragraph at lines 34--37 \OT1/cmr/m/n/10 fines the Selmer and the Shafarevich-Tate groups as $[]\OML/cmm /m/it/10 Sel\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 E=K\OT1/cmr/m/n/10 )[] = [] \OML/ cmm/m/it/10 f; []\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 E=K\OT1/cmr/m/n/10 ) = [] Overfull \hbox (38.55847pt too wide) detected at line 41 [] [] LaTeX Warning: Citation `MR31:3420' on page 2 undefined on input line 72. [2] Overfull \hbox (12.60565pt too wide) in paragraph at lines 116--120 [][]\OT1/cmr/m/n/10 Denote com-plex con-ju-ga-tion by $\OML/cmm/m/it/10 ^^\$\OT 1/cmr/m/n/10 . We will de-com-pose $\OML/cmm/m/it/10 E\OT1/cmr/m/n/10 (\OML/cmm /m/it/10 K\OT1/cmr/m/n/10 )$ into its eigenspaces [] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [3] LaTeX Warning: Citation `mccallum' on page 4 undefined on input line 154. Overfull \hbox (1.826pt too wide) in paragraph at lines 177--181 \OT1/cmr/m/n/10 3.3.\OT1/cmr/bx/n/10 Precision.[] []\OT1/cmr/m/n/10 In the cou rse of our com-pu-ta-tions of $[\OML/cmm/m/it/10 E\OT1/cmr/m/n/10 (\OML/cmm/m/i t/10 K\OT1/cmr/m/n/10 ) : \OT1/cmr/bx/n/10 Z\OML/cmm/m/it/10 y[]\OT1/cmr/m/n/10 ] = []$ [] LaTeX Warning: Citation `cremona-algorithms' on page 4 undefined on input line 189. LaTeX Warning: Citation `cremona-mwrank' on page 4 undefined on input line 191. LaTeX Warning: Citation `cremona-algorithms' on page 4 undefined on input line 193. LaTeX Warning: Citation `cremona-algorithms' on page 4 undefined on input line 195. [4] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [5] LaTeX Warning: Citation `grigor' on page 6 undefined on input line 328. Overfull \hbox (9.43153pt too wide) in paragraph at lines 328--330 [][]\OT1/cmr/m/n/10 For gen-eral $\OML/cmm/m/it/10 E$\OT1/cmr/m/n/10 , the rep- re-sen-ta-tion is sur-jec-tive when $\OML/cmm/m/it/10 p \OMS/cmsy/m/n/10 ^^U \O T1/cmr/m/n/10 1 + [] [][] []$ [] Overfull \hbox (17.0141pt too wide) in paragraph at lines 339--340 \OT1/cmr/m/n/10 rep-re-sen-ta-tion only to prove that $\OML/cmm/m/it/10 H[]\OT1 /cmr/m/n/10 (\OML/cmm/m/it/10 K\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 E\OT1/cmr/m/n/ 10 [\OML/cmm/m/it/10 p\OT1/cmr/m/n/10 ])\OML/cmm/m/it/10 =K; E\OT1/cmr/m/n/10 [ \OML/cmm/m/it/10 p\OT1/cmr/m/n/10 ]) = 0$ and $\OML/cmm/m/it/10 H[]\OT1/cmr/m/n /10 (\OML/cmm/m/it/10 K[]=K; E\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 K[]\OT1/cmr/m/n /10 )[\OML/cmm/m/it/10 p\OT1/cmr/m/n/10 ]) = [] LaTeX Warning: Citation `cha:kolyvagin' on page 6 undefined on input line 344. [6] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [7] Overfull \hbox (1.97957pt too wide) in paragraph at lines 434--435 [][]\OT1/cmr/m/n/10 Let $\OML/cmm/m/it/10 Z$ \OT1/cmr/m/n/10 be the sub-group o f scalars. Clearly $\OML/cmm/m/it/10 E\OT1/cmr/m/n/10 [\OML/cmm/m/it/10 p\OT1/c mr/m/n/10 ][] = 0$. Con-sider the Hochshild- [] Overfull \hbox (23.67772pt too wide) in paragraph at lines 483--484 \OT1/cmr/bx/n/10 Proposition 5.5. []\OT1/cmr/m/it/10 Sup-pose $\OML/cmm/m/it/10 E$ \OT1/cmr/m/it/10 has no $\OT1/cmr/bx/n/10 Q$\OT1/cmr/m/it/10 -rational $\OM L/cmm/m/it/10 p$\OT1/cmr/m/it/10 -isogeny. Then $\OML/cmm/m/it/10 H[]\OT1/cmr/m /n/10 (\OT1/cmr/bx/n/10 Q\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 E\OT1/cmr/m/n/10 [\O ML/cmm/m/it/10 p\OT1/cmr/m/n/10 ])\OML/cmm/m/it/10 =\OT1/cmr/bx/n/10 Q\OML/cmm/ m/it/10 ; E\OT1/cmr/m/n/10 [\OML/cmm/m/it/10 p\OT1/cmr/m/n/10 ]) = [] [8] Overfull \hbox (13.19362pt too wide) in paragraph at lines 515--517 \OT1/cmr/m/n/10 5.2.3.\OT1/cmr/m/it/10 Vanishing of Co-ho-mol-ogy Groups II.[] []\OT1/cmr/m/n/10 We will ver-ify that $\OML/cmm/m/it/10 H[]\OT1/cmr/m/n/10 (\ OML/cmm/m/it/10 K[]=K; E\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 K[]\OT1/cmr/m/n/10 )[ \OML/cmm/m/it/10 p\OT1/cmr/m/n/10 ]) = [] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [9] LaTeX Warning: Citation `MR92e:11050' on page 10 undefined on input line 638. LaTeX Warning: Citation `MR92a:11058' on page 10 undefined on input line 638. LaTeX Warning: Citation `MR87g:11061b' on page 10 undefined on input line 641. Overfull \hbox (8.92725pt too wide) in paragraph at lines 640--643 [][]\OT1/cmr/m/n/10 If $[][]\OML/cmm/m/it/10 L\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 E=\OT1/cmr/bx/n/10 Q\OT1/cmr/m/n/10 ) = 1$, then a re-sult of Wald-spurger ([[ ]]) does the trick\OT1/cmr/bx/n/10 [[Todo: [] LaTeX Warning: Citation `MR2020572' on page 10 undefined on input line 646. [10] LaTeX Warning: Citation `MR81i:12014' on page 11 undefined on input line 657. LaTeX Warning: Citation `MR2000a:11077' on page 11 undefined on input line 658. LaTeX Warning: Citation `MR2002a:11051' on page 11 undefined on input line 666. LaTeX Warning: Citation `perrin-riou' on page 11 undefined on input line 702. Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [11] LaTeX Warning: Citation `perrin-riou:thesis' on page 12 undefined on input line 722. LaTeX Font Info: Try loading font information for U+euf on input line 730. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Warning: Font shape `OT1/cmss/m/it' in size <10> not available (Font) Font shape `OT1/cmss/m/sl' tried instead on input line 758. [12] Overfull \hbox (22.6093pt too wide) in paragraph at lines 854--874 \OT1/cmr/m/n/10 (http://www.maths.nott.ac.uk/personal/jec/book/fulltext/index.h tml). \OT1/cmr/bx/n/10 [[Todo: move [] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [13] LaTeX Warning: Citation `MR2004g:11045' on page 14 undefined on input line 896. LaTeX Warning: Citation `cremona:algorithms' on page 14 undefined on input line 908. [14] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [15] [16] Overfull \hbox (5.52495pt too wide) in paragraph at lines 1124--1124 []\OT1/cmtt/m/n/10 563 A 1 0 2 2 0.48 [0,0] [0,0] [1,1,1,-15 ,16][] [] Overfull \hbox (5.52495pt too wide) in paragraph at lines 1124--1124 []\OT1/cmtt/m/n/10 655 A 1 0 2 2 0.47 [0,0] [0,0] [0,0,1,-13 ,18][] [] Overfull \hbox (5.52495pt too wide) in paragraph at lines 1124--1124 []\OT1/cmtt/m/n/10 707 A 1 0 2 2 0.53 [0,0] [0,0] [0,1,1,-12 ,12][] [] Overfull \hbox (5.52495pt too wide) in paragraph at lines 1124--1124 []\OT1/cmtt/m/n/10 944 E 1 0 2 2 0.54 [0,0] [0,0] [0,0,0,-19 ,34][] [] Overfull \hbox (5.52495pt too wide) in paragraph at lines 1124--1124 []\OT1/cmtt/m/n/10 997 B 1 0 2 2 0.47 [0,0] [0,0] [0,-1,1,-5 ,-3][] [] Overfull \hbox (10.7749pt too wide) in paragraph at lines 1124--1124 []\OT1/cmtt/m/n/10 997 C 1 0 2 2 0.44 [0,0] [0,0] [0,-1,1,-2 4,54][] [] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [17] [18] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [19] Underfull \vbox (badness 10000) has occurred while \output is active [] [20] Underfull \vbox (badness 10000) has occurred while \output is active [] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [21] [22] Overfull \hbox (166.24414pt too wide) has occurred while \output is active [][] \OT1/cmr/m/n/7 COMPUTATIONAL VERIFICATION OF THE FULL BIRCH AND SWINNERTON -DYER CONJECTURE FOR CERTAIN ELLIPTIC CURVES [] [] [23] (./bsd01.aux) LaTeX Warning: There were undefined references. ) Here is how much of TeX's memory you used: 5777 strings out of 95755 68432 string characters out of 1194953 166802 words of memory out of 1000001 8522 multiletter control sequences out of 10000+50000 14513 words of font info for 58 fonts, out of 500000 for 1000 175 hyphenation exceptions out of 1000 39i,15n,40p,821b,394s stack positions out of 1500i,500n,5000p,200000b,5000s Output written on bsd01.dvi (23 pages, 123420 bytes).