\contentsline {section}{\numberline {1}\relax \fontsize {24.88}{30}\selectfont {\def 0 setgray{0. 0. 0.8 setrgbcolor}\special {ps: 0. 0. 0.8 setrgbcolor}\aftergroup \special {ps: 0 setgray}Contents}}{3}{section.1}
\contentsline {section}{\numberline {2}\relax \fontsize {24.88}{30}\selectfont {\def 0 setgray{0. 0. 0.8 setrgbcolor}\special {ps: 0. 0. 0.8 setrgbcolor}\aftergroup \special {ps: 0 setgray}The Birch and Swinnerton-Dyer Conjecture}}{4}{section.2}
\contentsline {section}{\numberline {3}\relax \fontsize {24.88}{30}\selectfont {\def 0 setgray{0. 0. 0.8 setrgbcolor}\special {ps: 0. 0. 0.8 setrgbcolor}\aftergroup \special {ps: 0 setgray}Status of Motivating Problem 1}}{5}{section.3}
\contentsline {section}{\numberline {4}\relax \fontsize {24.88}{30}\selectfont {\def 0 setgray{0. 0. 0.8 setrgbcolor}\special {ps: 0. 0. 0.8 setrgbcolor}\aftergroup \special {ps: 0 setgray}Verify BSD For Conductor $\leq 1000$}}{6}{section.4}
\contentsline {section}{\numberline {5}\relax \fontsize {24.88}{30}\selectfont {\def 0 setgray{0. 0. 0.8 setrgbcolor}\special {ps: 0. 0. 0.8 setrgbcolor}\aftergroup \special {ps: 0 setgray}Rank $2$}}{7}{section.5}
\contentsline {section}{\numberline {6}\relax \fontsize {24.88}{30}\selectfont {\def 0 setgray{0. 0. 0.8 setrgbcolor}\special {ps: 0. 0. 0.8 setrgbcolor}\aftergroup \special {ps: 0 setgray}The Plan}}{8}{section.6}
\contentsline {section}{\numberline {7}\relax \fontsize {24.88}{30}\selectfont {\def 0 setgray{0. 0. 0.8 setrgbcolor}\special {ps: 0. 0. 0.8 setrgbcolor}\aftergroup \special {ps: 0 setgray}Refined Kolyvagin Theorem}}{9}{section.7}
\contentsline {section}{\numberline {8}\relax \fontsize {24.88}{30}\selectfont {\def 0 setgray{0. 0. 0.8 setrgbcolor}\special {ps: 0. 0. 0.8 setrgbcolor}\aftergroup \special {ps: 0 setgray}Algorithm}}{10}{section.8}
\contentsline {section}{\numberline {9}\relax \fontsize {24.88}{30}\selectfont {\def 0 setgray{0. 0. 0.8 setrgbcolor}\special {ps: 0. 0. 0.8 setrgbcolor}\aftergroup \special {ps: 0 setgray}Result of Running the Algorithm}}{11}{section.9}
\contentsline {subsection}{\numberline {9.1}A Potentially Serious Obstruction}{16}{subsection.9.1}