This is e-TeX, Version 3.14159-2.1 (Web2C 7.4.5) entering extended mode LaTeX2e <2001/06/01> Babel and hyphenation patterns for american, nohyphenation, loaded. (./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 (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. 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Loading kernel: messages; fonts; allocations: state, direction, utility macros; pictures: \xy, positions, objects, decorations; kernel objects: directionals, circles, text; options; algorithms: directions, edges, connections; Xy-pic loaded) (/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, circles, 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 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 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} (./macros.tex (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty) (/usr/share/texmf/tex/latex/hyperref/hyperref.sty (/usr/share/texmf/tex/latex/graphics/keyval.sty) (/usr/share/texmf/tex/latex/hyperref/pd1enc.def) (/usr/share/texmf/tex/latex/config/hyperref.cfg) Implicit mode ON; LaTeX internals redefined (/usr/share/texmf/tex/latex/misc/url.sty)) *hyperref using driver hypertex* (/usr/share/texmf/tex/latex/hyperref/hypertex.def)) :<- (./bsd01.aux) (/usr/share/texmf/tex/latex/cyrillic/ot2cmr.fd) (/usr/share/texmf/tex/latex/amsfonts/umsa.fd) (/usr/share/texmf/tex/latex/amsfonts/umsb.fd) (/usr/share/texmf/tex/latex/hyperref/nameref.sty) (/usr/share/texmf/tex/latex/base/omscmr.fd) (./bsd01.toc (/usr/share/texmf/tex/latex/cyrillic/ot2wncyr.fd)) [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 (24.06026pt too wide) detected at line 290 \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 ]) \OMS /cmsy/m/n/10 ! \OML/cmm/m/it/10 H[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 K; E\OT1/c mr/m/n/10 [\OML/cmm/m/it/10 p\OT1/cmr/m/n/10 ]) \OMS/cmsy/m/n/10 ! \OML/cmm/m/i t/10 H[]\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 ])[] \OMS/cmsy/m/n/10 ! \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 ])\OML/cmm/m/it/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 [] [5] LaTeX Warning: Citation `grigor' on page 6 undefined on input line 320. Overfull \hbox (9.43153pt too wide) in paragraph at lines 320--321 [][]\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 330--331 \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 335. [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 395--396 [][]\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- [8] Overfull \hbox (23.67772pt too wide) in paragraph at lines 436--437 \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 ]) = 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] Overfull \hbox (6.99559pt too wide) in paragraph at lines 526--531 \OT1/cmr/m/n/10 now fol-low from the Hochschild-Serre spec-tral se-quence $[]\O ML/cmm/m/it/10 H[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 P[]; H[]\OT1/cmr/m/n/10 (\O ML/cmm/m/it/10 P; E\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 L\OT1/cmr/m/n/10 )[\OML/cm m/m/it/10 p\OT1/cmr/m/n/10 ][])) =[]\OMS/cmsy/m/n/10 ) [10] LaTeX Warning: Citation `MR92e:11050' on page 11 undefined on input line 574. LaTeX Warning: Citation `MR92a:11058' on page 11 undefined on input line 574. LaTeX Warning: Citation `MR87g:11061b' on page 11 undefined on input line 576. LaTeX Warning: Citation `MR2020572' on page 11 undefined on input line 580. LaTeX Warning: Citation `MR81i:12014' on page 11 undefined on input line 582. LaTeX Warning: Citation `MR2000a:11077' on page 11 undefined on input line 582. LaTeX Warning: Citation `MR2002a:11051' on page 11 undefined on input line 582. 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' on page 12 undefined on input line 592. LaTeX Warning: Citation `perrin-riou:thesis' on page 12 undefined on input line 606. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd) [12] 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 641. 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 774. LaTeX Warning: Citation `cremona:algorithms' on page 14 undefined on input line 785. [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 1001--1001 []\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 1001--1001 []\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 1001--1001 []\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 1001--1001 []\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 1001--1001 []\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 1001--1001 []\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. ) (see the transcript file for additional information) Output written on bsd01.dvi (23 pages, 123448 bytes). 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