ELLIPTIC CURVES 
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Mi 1.6. Dekan,  di.14.4- Mi22.6 OP  
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&Uuml;bung Mi 29.6. entf&auml;lt wegen New Work Auftaktgespr&auml;ch
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Lectures: Di 14:15-15:45 Geom H4 & Do 12:15-13:45 Geom H3
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Exercises: Mi 10:15-11:45 Geom 431   
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Exams: Each particioant has to give a talk in the exercise classes  and there will
be an extra homework, resp. TakeHomeExam, at the end of the semester, which will be the basis for an oral examinination
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Topics for the extra talks  (each for a team of 2 persons):
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Archimedes Cattle problem and the Pell equation: <a href="https://www.math.nyu.edu/~crorres/Archimedes/Cattle/cattle_vardi.pdf">I. Vardi </a>
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The Congruent Number Problem and elliptic curves:  <a href="http://www.math.rug.nl/~top/Chandrasekar.pdf">V. Chandesakar</a>  
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A survey on Elliptic surfaces: J. Silverman; <a href="https://arxiv.org/abs/0907.0298">M. Sch&uuml;tt, T. Shioda</a>
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Counting covers of elliptic curves: <a href="http://people.mpim-bonn.mpg.de/zagier/files/progmath/129/165/fulltext.pdf ">M. Kaneko, D. Zagier</a>; <a href="https://orlandomarigliano.com/bachelors-thesis.pdf">O. Marigliano BSc-thesis</a>;  <a href="https://mast.queensu.ca/~mikeroth/ ">M. Roth, Notes and Maple program</a>

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Literature:
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J. Milne: Elliptic curves
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J. Silverman: The arithmetic of ellptic curves
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A. Knapp: Elliptic curves
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Software tools to study elliptic curves:
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<a href="https://www.geogebra.org/m/mmhehfqs">Gruppenoperation auf elliptischen Kurven mit GeoBra</a>
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<a href="https://pari.math.u-bordeaux.fr/dochtml/html/Elliptic_curves.html">Elliptic curves in Pari/GP</a>
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<a href="https://doc.sagemath.org/html/en/reference/arithmetic_curves/index.html">Elliptic curves in Sage</a>

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Additional literature:	
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K. Ueno: Algebraic geometry I-III, AMS
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K. Hulek: Elementare algebraische Geometrie, Springer Spektrum
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R. Hartshorne: Algebraic Geometry, GTM Springer
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D. Mumford: The Red book of Varieties ans Schemes, LNM Springer
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M. Miyanishi: Algebraic Geometry, AMS
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D. Perrin: Geometrie algebrique, CNRS
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U. G&ouml;rtz, T. Wedhorn: Algebraic Geometry, Vieweg
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Q. Liu: Arithmetic and algebraic curves, Oxford