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biblio.bib
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@book{marcus1977number,
title={Number {F}ields},
author={Marcus, Daniel A.},
isbn={9780387902791},
lccn={77021467},
series={Universitext (1979)},
url={https://books.google.com/books?id=qMfGgJPCnVMC},
year={1977},
publisher={Springer}
}
@article{sqrt5first,
AUTHOR = {Bober, J. and Deines, A. and Klages-Mundt, A. and LeVeque, B. and Ohana, R. A. and Rabindranath, A. and Sharaba, P. and Stein, W.},
TITLE = {A {D}atabase of {E}lliptic {C}urves over {$\mathbf{Q}(\sqrt{5})$}---{F}irst {R}eport},
JOURNAL = {Proceedings of the 10th International Symposium (ANTS-X)},
PUBLISHER = {Springer-Verlag},
YEAR = {2012}
}
@incollection{greenberg:iwasawa-padic,
AUTHOR = {Greenberg, Ralph},
TITLE = {Iwasawa theory for {$p$}-adic representations},
BOOKTITLE = {Algebraic number theory},
SERIES = {Adv. Stud. Pure Math.},
VOLUME = {17},
PAGES = {97--137},
PUBLISHER = {Academic Press},
ADDRESS = {Boston, MA},
YEAR = {1989}
}
@book {MR1097604,
TITLE = {Algebraic number theory},
SERIES = {Adv. Stud. Pure Math.},
VOLUME = {17},
EDITOR = {Coates, J. and Greenberg, R. and Mazur, B. and Satake, I.},
NOTE = {Papers in honor of K. Iwasawa on the occasion of his 70th
birthday on September 11, 1987},
PUBLISHER = {Academic Press Inc.},
ADDRESS = {Boston, MA},
YEAR = {1989},
PAGES = {xxvi+492},
ISBN = {0-12-177370-1},
}
@article {ritter-weiss:main,
AUTHOR = {Ritter, J{\"u}rgen and Weiss, Alfred},
TITLE = {On the ``main conjecture'' of equivariant {I}wasawa theory},
JOURNAL = {J. Amer. Math. Soc.},
FJOURNAL = {Journal of the American Mathematical Society},
VOLUME = {24},
YEAR = {2011},
NUMBER = {4},
PAGES = {1015--1050},
ISSN = {0894-0347},
MRCLASS = {11R23 (11R42 11S40 19F99)},
DOI = {10.1090/S0894-0347-2011-00704-2},
}
@article {greenberg:selmer,
AUTHOR = {Greenberg, Ralph},
TITLE = {Surjectivity of the global-to-local map defining a {S}elmer
group},
JOURNAL = {Kyoto J. Math.},
FJOURNAL = {Kyoto Journal of Mathematics},
VOLUME = {50},
YEAR = {2010},
NUMBER = {4},
PAGES = {853--888},
ISSN = {2156-2261},
MRCLASS = {11R34 (11G05 11G10)},
MRNUMBER = {2740696 (2012a:11177)},
MRREVIEWER = {Fabrizio Andreatta},
DOI = {10.1215/0023608X-2010-016},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.1215/0023608X-2010-016},
}
@article {velu:isogenies,
AUTHOR = {V{\'e}lu, Jacques},
TITLE = {Isog\'enies entre courbes elliptiques},
JOURNAL = {C. R. Acad. Sci. Paris S\'er. A-B},
VOLUME = {273},
YEAR = {1971},
PAGES = {A238--A241},
MRCLASS = {14H99},
MRREVIEWER = {J. C. Fogarty},
}
@article {billerey:isog,
AUTHOR = {Billerey, Nicolas},
TITLE = {Crit\`eres d'irr\'eductibilit\'e pour les repr\'esentations
des courbes elliptiques},
JOURNAL = {Int. J. Number Theory},
FJOURNAL = {International Journal of Number Theory},
VOLUME = {7},
YEAR = {2011},
NUMBER = {4},
PAGES = {1001--1032},
ISSN = {1793-0421},
MRCLASS = {11G05 (11F80 11R37)},
MRNUMBER = {2812649},
DOI = {10.1142/S1793042111004538}
}
@article {cremona:abvar,
AUTHOR = {Cremona, J. E.},
TITLE = {Abelian varieties with extra twist, cusp forms, and elliptic
curves over imaginary quadratic fields},
JOURNAL = {J. London Math. Soc. (2)},
FJOURNAL = {Journal of the London Mathematical Society. Second Series},
VOLUME = {45},
YEAR = {1992},
NUMBER = {3},
PAGES = {404--416},
ISSN = {0024-6107},
CODEN = {JLMSAK},
MRCLASS = {11G10 (11F12 11F30 11F66 11G05)},
MRNUMBER = {1180252 (93h:11056)},
MRREVIEWER = {Henri Darmon},
DOI = {10.1112/jlms/s2-45.3.404},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.1112/jlms/s2-45.3.404},
}
@article {gross-kudla,
AUTHOR = {Gross, Benedict H. and Kudla, Stephen S.},
TITLE = {Heights and the central critical values of triple product
{$L$}-functions},
JOURNAL = {Compositio Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {81},
YEAR = {1992},
NUMBER = {2},
PAGES = {143--209},
ISSN = {0010-437X},
CODEN = {CMPMAF},
MRCLASS = {11F66 (11F67 11G40 19F27)},
MRNUMBER = {1145805 (93g:11047)},
MRREVIEWER = {Alexey A. Panchishkin},
NOTE = {\url{https://www.numdam.org.offcampus.lib.washington.edu/item?id=CM_1992__81_2_143_0}},
}
}
@article{gsl,
AUTHOR = {GSL},
TITLE = {{GNU Scientific Library}},
NOTE = {\url{https://www.gnu.org/s/gsl/}},
YEAR = {2011}
}
@article{darmon_rotger_sols:iterated,
AUTHOR = {Darmon, Henri and Rotger, Victor and Sols, Ignacio},
TITLE = {Iterated integrals, diagonal cycles and rational points on elliptic curves},
journal = {Preprint},
YEAR = {2011},
NOTE = {\url{https://www-ma2.upc.edu/vrotger/docs/DRS1.pdf}}
}
@article {darmon_daub_lichtenstein_rotger:chow_heegner,
AUTHOR = {Darmon, Henri and Daub, Michael and Lichtenstein, Sam and Rotger, Victor},
TITLE = {The {E}ffective {C}omputation of {I}terated {I}ntegrals and {C}how-{H}eegner {P}oints on {T}riple {P}roducts},
journal = {In Preparation},
YEAR = {2011}
}
@article {gee:lifting,
AUTHOR = {Gee, Toby},
TITLE = {A modularity lifting theorem for weight two {H}ilbert modular
forms},
JOURNAL = {Math. Res. Lett.},
FJOURNAL = {Mathematical Research Letters},
VOLUME = {13},
YEAR = {2006},
NUMBER = {5-6},
PAGES = {805--811},
ISSN = {1073-2780},
MRCLASS = {11F33 (11F41 11F80)},
MRNUMBER = {2280776 (2007m:11065)},
MRREVIEWER = {David L. Savitt},
}
@article {kisin:moduli,
AUTHOR = {Kisin, Mark},
TITLE = {Moduli of finite flat group schemes, and modularity},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {170},
YEAR = {2009},
NUMBER = {3},
PAGES = {1085--1180},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {11F80 (11R39 14L15)},
MRNUMBER = {2600871 (2011g:11107)},
MRREVIEWER = {David L. Savitt},
DOI = {10.4007/annals.2009.170.1085},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.4007/annals.2009.170.1085},
}
@article{fisher:families_cong,
AUTHOR = {Fisher, Tom},
TITLE = {On {F}amilies of $n$-congruent {E}lliptic {C}urves},
Journal = {Preprint},
Year = 2011
}
@manual{psage,
Key = {Sage},
Author = {W.\thinspace{}A. Stein and others},
Title = {PSAGE {L}ibrary},
note = {\url{https://code.google.com/p/purplesage/}},
Year = {2011},
}
@article{pollack-stevens:overconv,
AUTHOR={Pollack, Robert and Stevens, Glenn},
TITLE = {Overconvergent {M}odular {S}ymbols and $p$-adic {$L$}-functions},
JOURNAL = {Annales Scientifiques de l'Ecole Normale Superieure},
year = {to appear}
}
@article{coates:enigmatic,
AUTHOR = {Coates, John},
TITLE = {The enigmatic {T}ate-{S}hafarevich group},
JOURNAL = {2010 Proceedings of International Congress of Chinese Mathematicians},
YEAR = 2011,
}
@article {greenberg-vatsal:iwasawa,
AUTHOR = {Greenberg, Ralph and Vatsal, Vinayak},
TITLE = {On the {I}wasawa invariants of elliptic curves},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {142},
YEAR = {2000},
NUMBER = {1},
PAGES = {17--63},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {11R23 (11G05)},
MRNUMBER = {1784796 (2001g:11169)},
MRREVIEWER = {Jacques Tilouine},
DOI = {10.1007/s002220000080},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.1007/s002220000080},
}
@incollection {greenberg:intro_iwasawa,
AUTHOR = {Greenberg, Ralph},
TITLE = {Introduction to {I}wasawa theory for elliptic curves},
BOOKTITLE = {Arithmetic algebraic geometry ({P}ark {C}ity, {UT}, 1999)},
SERIES = {IAS/Park City Math. Ser.},
VOLUME = {9},
PAGES = {407--464},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {2001},
MRCLASS = {11G05 (11G40 11R23 11R34)},
MRNUMBER = {1860044 (2003a:11067)},
MRREVIEWER = {Massimo Bertolini},
}
@book {MR1860012,
TITLE = {Arithmetic algebraic geometry},
SERIES = {IAS/Park City Mathematics Series},
VOLUME = {9},
EDITOR = {Conrad, Brian and Rubin, Karl},
NOTE = {Including papers from the Graduate Summer School of the
Institute for Advanced Study/Park City Mathematics Institute
held in Park City, UT, June 20--July 10, 1999},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2001},
PAGES = {xiv+569},
ISBN = {0-8218-2173-3},
MRCLASS = {11-06 (14-06)},
MRNUMBER = {1860012 (2002d:11003)},
}
@article{skinner-urban,
AUTHOR = {Skinner, C. and Urban, D.},
title = {The {I}wasawa {M}ain {C}onjecture for {${\rm GL}_2$}},
year = {2010},
note = {\url{https://www.math.columbia.edu/\%7Eurban/eurp/MC.pdf}}
}
@article {coates-liang-sujatha:cm_sha2,
AUTHOR = {Coates, J. and Liang, Z. and Sujatha, R.},
TITLE = {The {T}ate-{S}hafarevich group for elliptic curves with
complex multiplication {II}},
JOURNAL = {Preprint},
YEAR = {2010},
note = {\url{https://arxiv.org/abs/1005.4206}}
}
@article {coates-liang-sujatha:cm_sha,
AUTHOR = {Coates, J. and Liang, Z. and Sujatha, R.},
TITLE = {The {T}ate-{S}hafarevich group for elliptic curves with
complex multiplication},
JOURNAL = {J. Algebra},
FJOURNAL = {Journal of Algebra},
VOLUME = {322},
YEAR = {2009},
NUMBER = {3},
PAGES = {657--674},
ISSN = {0021-8693},
CODEN = {JALGA4},
MRCLASS = {11G05 (11G15)},
MRNUMBER = {2531216 (2010e:11052)},
MRREVIEWER = {Remke Kloosterman},
DOI = {10.1016/j.jalgebra.2009.04.039},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.1016/j.jalgebra.2009.04.039},
}
@article {cremona-fisher-oneil-simon-stoll:n-descent,
AUTHOR = {Cremona, J. E. and Fisher, T. A. and O'Neil, C. and Simon, D.
and Stoll, M.},
TITLE = {Explicit {$n$}-descent on elliptic curves. {I}. {A}lgebra},
JOURNAL = {J. Reine Angew. Math.},
FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's
Journal]},
VOLUME = {615},
YEAR = {2008},
PAGES = {121--155},
ISSN = {0075-4102},
CODEN = {JRMAA8},
MRCLASS = {11G05 (11R34 11Y50 14G25)},
MRNUMBER = {2384334 (2009g:11067)},
MRREVIEWER = {Imin Chen},
DOI = {10.1515/CRELLE.2008.012},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.1515/CRELLE.2008.012},
}
@article{sutherland:16,
author = {Sutherland, Andrew},
title = {Email: surjective $p$-adic repn for some rank $2$ curves},
year = {2010},
journal = {Personal Communication},
note = {\url{https://wstein.org/papers/bib/2010-sutherland-16.txt}}
}
@article{bradshaw-stein:heegner,
author = {Bradshaw, R. and Stein, W.\thinspace{}A.},
title = {Heegner {P}oints and the {A}rithmetic of {E}lliptic {C}urves over {R}ing {C}lass {E}xtensions},
year = {2011},
journal = {Submitted},
note = {\url{https://wstein.org/papers/bs-heegner/}}
}
@article{elkies:2010-3,
author = {Elkies, Noam},
title = {Email: surjective $p$-adic repn for some rank 2 curves},
year = {2010},
journal = {Personal Communication},
note = {\url{https://wstein.org/papers/bib/2010-elkies-3.txt}}
}
@article{ribet:2010-eis,
author = {Ribet, Kenneth A.},
title = {Email: supersingular points on elliptic curves modulo $\ell$},
year = {2010},
journal = {Personal Communication},
note = {\url{https://wstein.org/papers/bib/2010-ribet-eis.txt}}
}
@article{bhargava-shankar:avgrank,
author = {Bhargava, M. and Shankar, A.},
title = {Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves},
year = {2010},
journal = {Preprint},
note = {\url{https://arxiv.org/abs/1006.1002}}
}
@article{voight:matrix,
AUTHOR = {Voight, John},
TITLE = {Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms},
NOTE = {\url{https://arxiv.org/abs/1004.0994} or \url{https://www.cems.uvm.edu/~voight/articles/quatalgs-040110.pdf}},
JOURNAL = {Submitted}
}
@article {emerton:supersingular,
AUTHOR = {Emerton, Matthew},
TITLE = {Supersingular elliptic curves, theta series and weight two
modular forms},
JOURNAL = {J. Amer. Math. Soc.},
FJOURNAL = {Journal of the American Mathematical Society},
VOLUME = {15},
YEAR = {2002},
NUMBER = {3},
PAGES = {671--714 (electronic)},
ISSN = {0894-0347},
MRCLASS = {11F11 (11F27 11G05)},
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@book {lang:elliptic,
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@book {washington:cyclo,
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YEAR = {2010}
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}
@article {bertolini-darmon,
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}
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AUTHOR = {Robert Bradshaw},
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JOURNAL = {University of Washington Ph.D. Thesis under William Stein},
YEAR = {2010}
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@article {sd22,
TITLE = {{S}age {D}ays 22: {C}omputing with {E}lliptic {C}urves},
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YEAR={2010}
}
@article{hopkins:phd,
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JOURNAL = {Experiment. Math.},
FJOURNAL = {Experimental Mathematics},
YEAR={2010},
NOTE = {\url{https://www.ma.utexas.edu/users/khopkins/Hopkins-Heg.pdf}}
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AUTHOR = {{\c{C}}iperiani, Mirela and Wiles, Andrew},
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JOURNAL = {Duke Math. J.},
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DOI = {10.1215/00127094-2008-010},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.1215/00127094-2008-010},
note = {\url{https://www.ma.utexas.edu/users/mirela/solvable.pdf}}
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@article{sage:workshops,
TITLE = {List of {S}age {W}orkshops},
AUTHOR = {William Stein},
NOTE = {\url{https://wiki.sagemath.org/Workshops}}
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@article{stein:blog,
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AUTHOR = {T. Dokchitser and V. Dokchitser}
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@article {sd17,
TITLE = {{S}age {D}ays 17: {C}omputing with {M}odular {F}orms and {$L$}-functions},
NOTE = {\url{https://wiki.sagemath.org/days17}},
YEAR={2009}
}
@proceedings {MR2281142,
TITLE = {Algorithmic number theory},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {4076},
BOOKTITLE = {Proceedings of the 7th {I}nternational {S}ymposium
({ANTS}-{VII}) held at the {T}echnische {U}niversit\"at
{B}erlin, {B}erlin, {J}uly 23--28, 2006},
EDITOR = {Hess, Florian and Pauli, Sebastian and Pohst, Michael},
PUBLISHER = {Springer-Verlag},
ADDRESS = {Berlin},
YEAR = {2006},
PAGES = {x+598},
ISBN = {978-3-540-36075-9; 3-540-36075-1},
MRCLASS = {11-06 (11Y16)},
MRNUMBER = {2281142 (2007h:11001)},
DOI = {10.1007/11792086},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.1007/11792086},
}
@incollection {voight:cm,
AUTHOR = {Voight, John},
TITLE = {Computing {CM} points on {S}himura curves arising from
cocompact arithmetic triangle groups},
BOOKTITLE = {Algorithmic number theory},
SERIES = {Lecture Notes in Comput. Sci.},
VOLUME = {4076},
PAGES = {406--420},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2006},
MRCLASS = {11G18 (11G15 14G35)},
MRNUMBER = {2282939 (2008g:11104)},
MRREVIEWER = {Montserrat Alsina},
DOI = {10.1007/11792086_29},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.1007/11792086_29},
}
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VOLUME = {85},
YEAR = {1967},
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MRCLASS = {14.49 (10.68)},
MRNUMBER = {0204426 (34 \#4268)},
MRREVIEWER = {M. Eichler},
}
@article{greenberg-voight:shimura,
TITLE = {Computing systems of Hecke eigenvalues associated to Hilbert modular forms},
AUTHOR = {Greenberg, Matthew and Voight, John},
NOTE = {\url{https://www.cems.uvm.edu/~voight/articles/heckefun-021910.pdf}},
YEAR = {2010},
JOURNAL = {Math. Comp.},
FJOURNAL = {Mathematics of Computation}
}
@article{delaunay:thesis,
AUTHOR = {Delaunay, Christophe},
TITLE = {Formes modulaires et invariants de courbes elliptiques
d\'efinies sur $\mathbf{Q}$},
YEAR = {2002},
NOTE = {Th\`ese de Doctorat, Universit\'e Bordeaux I, available at \url{https://math.univ-lyon1.fr/~delaunay/}}
}
@article {voight:shimura2,
AUTHOR = {Voight, John},
TITLE = {Shimura curves of genus at most two},
JOURNAL = {Math. Comp.},
FJOURNAL = {Mathematics of Computation},
VOLUME = {78},
YEAR = {2009},
NUMBER = {266},
PAGES = {1155--1172},
ISSN = {0025-5718},
CODEN = {MCMPAF},
MRCLASS = {11G18 (11R52)},
MRNUMBER = {2476577 (2010h:11099)},
MRREVIEWER = {Imin Chen},
DOI = {10.1090/S0025-5718-08-02163-7},
URL = {https://dx.doi.org.offcampus.lib.washington.edu/10.1090/S0025-5718-08-02163-7},
}
@article{gross:msri2001,
author= {Gross, B.\thinspace{}H.},
year = {2001},
TITLE = {Heegner points and {R}ankin {$L$}-series, 1980-1987},
note = {\url{https://www.msri.org/publications/ln/msri/2001/rankin-L/gross/1/index.html}}
}
@article{birch:msri2001,
AUTHOR={Bryan Birch},
year = {2001},
TITLE = {Heegner points: {T}he beginnings},