Reinier Bröker

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All published works

Action	Title	Year	Authors
+ PDF Chat	Explicit computations in Iwasawa theory	2019	Reinier Bröker David Hubbard Lawrence C. Washington
+ PDF Chat	Fourier coefficients of sextic theta series	2015	Reinier Bröker Jeffrey Hoffstein
+ PDF Chat	Genus-2 curves and Jacobians with a given number of points	2015	Reinier Bröker Everett W. Howe Kristin Lauter Peter Stevenhagen
+ PDF Chat	Evaluating Igusa functions	2014	Reinier Bröker Kristin Lauter
+	Fourier coefficients of sextic theta series	2013	Reinier Bröker Jeffrey Hoffstein
+	Abelian surfaces admitting an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-endomorphism	2013	Reinier Bröker Kristin Lauter Marco Streng
+	Fourier coefficients of sextic theta series	2013	Reinier Bröker Jeffrey Hoffstein
+ PDF Chat	Explicit CM theory for level 2-structures on abelian surfaces	2011	Reinier Bröker David Gruenewald Kristin Lauter
+ PDF Chat	Modular polynomials via isogeny volcanoes	2011	Reinier Bröker Kristin Lauter Andrew V. Sutherland
+	Abelian surfaces admitting an (l,l)-endomorphism	2011	Reinier Bröker Kristin Lauter Marco Streng
+ PDF Chat	<i>p</i>-adic class invariants	2011	Reinier Bröker
+	Abelian surfaces admitting an (l,l)-endomorphism	2011	Reinier Bröker Kristin Lauter Marco Streng
+	Evaluating Igusa functions	2010	Reinier Bröker Kristin Lauter
+ PDF Chat	An explicit height bound for the classical modular polynomial	2010	Reinier Bröker Andrew V. Sutherland
+	Evaluating Igusa functions	2010	Reinier Bröker Kristin Lauter
+	Explicit CM-theory in dimension 2	2009	Reinier Bröker David Gruenewald Kristin Lauter
+	Explicit CM-theory for level 2-structures on abelian surfaces	2009	Reinier Bröker David Gruenewald Kristin Lauter
+ PDF Chat	Modular Polynomials for Genus 2	2009	Reinier Bröker Kristin Lauter
+	Explicit CM-theory for level 2-structures on abelian surfaces	2009	Reinier Bröker David A. Gruenewald Kristin Lauter
+	Constructing elliptic curves of prescribed order	2008	Reinier Bröker
+ PDF Chat	A $p$-adic algorithm to compute the Hilbert class polynomial	2008	Reinier Bröker
+	Modular polynomials for genus 2	2008	Reinier Bröker Kristin Lauter
+ PDF Chat	Computing Hilbert Class Polynomials	2008	Juliana Belding Reinier Bröker Andreas Enge Kristin Lauter
+	Constructing elliptic curves of prime order	2008	Reinier Bröker Peter Stevenhagen
+	Computing Hilbert Class Polynomials	2008	Juliana Belding Reinier Bröker Andreas Enge Kristin Lauter
+	Modular polynomials for genus 2	2008	Reinier Bröker Kristin Lauter
+	Computing Hilbert Class Polynomials.	2008	Juliana Belding Reinier Bröker Andreas Enge Kristin Lauter
+ PDF Chat	Efficient CM-constructions of elliptic curves over finite fields	2007	Reinier Bröker Peter Stevenhagen
+	Constructing elliptic curves of prime order	2007	Reinier Bröker Peter Stevenhagen
+	Constructing elliptic curves in almost polynomial time	2005	Reinier Bröker Peter Stevenhagen
+	Elliptic Curves with a Given Number of Points	2004	Reinier Bröker Peter Stevenhagen

Common Coauthors

Coauthor	Papers Together
Kristin Lauter	18
Peter Stevenhagen	6
Jeffrey Hoffstein	3
David Gruenewald	3
Andreas Enge	3
Marco Streng	3
Juliana Belding	3
Andrew V. Sutherland	2
Lawrence C. Washington	1
David Hubbard	1
David A. Gruenewald	1
Everett W. Howe	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Action of Modular Correspondences around CM Points	2002	Jean-Marc Couveignes Thiérry Hénocq	11
+	A Course in Computational Algebraic Number Theory	1993	Henri Cohen	8
+	Handbook of Elliptic and Hyperelliptic Curve Cryptography	2005	Henri Cohen Gerhard Frey Roberto Avanzi Christophe Doche Tanja Lange Kim Nguyễn Fréderik Vercauteren	7
+ PDF Chat	A $p$-adic algorithm to compute the Hilbert class polynomial	2008	Reinier Bröker	7
+ PDF Chat	The complexity of class polynomial computation via floating point approximations	2008	Andreas Enge	7
+ PDF Chat	Computing Hilbert Class Polynomials	2008	Juliana Belding Reinier Bröker Andreas Enge Kristin Lauter	7
+	Constructing elliptic curves of prescribed order	2008	Reinier Bröker	6
+	Isogeny Volcanoes and the SEA Algorithm	2002	Mireille Fouquet François Morain	6
+	Hilbert’s 12th Problem, Complex Multiplication and Shimura Reciprocity	2018	Peter Stevenhagen	6
+ PDF Chat	Constructing elliptic curves over finite fields using double eta-quotients	2004	Andreas Enge Reinhard Schertz	5
+ PDF Chat	Weber's class invariants revisited	2002	Reinhard Schertz	5
+	The Magma Algebra System I: The User Language	1997	Wieb Bosma John Cannon Catherine Playoust	5
+ PDF Chat	Constructing hyperelliptic curves of genus 2 suitable for cryptography	2002	Annegret Weng	5
+ PDF Chat	Elliptic curves over finite fields and the computation of square roots mod 𝑝	1985	René Schoof	5
+	Abelian Varieties with Complex Multiplication and Modular Functions	1998	Goro Shimura	5
+	The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography	2006	Pierrick Gaudry Thomas Houtmann David Kohel Christophe Ritzenthaler Annegret Weng	5
+	Modular Forms and Projective Invariants	1967	Jun-ichi Igusa	5
+	On Siegel Modular Forms of Genus Two	1962	Jun-ichi Igusa	5
+ PDF Chat	The Arithmetic of Elliptic Curves	1986	Joseph H. Silverman	5
+	The exponents of the groups of points on the reductions of an elliptic curve	1991	René Schoof	4
+	Construction de courbes de genre 2 à partir de leurs modules	1991	Jean-François Mestre	4
+	A CRT algorithm for constructing genus 2 curves over finite fields	2004	Kirsten Eisentr Kristin Lauter	4
+ PDF Chat	Constructing elliptic curves with a known number of points over a prime field	2004	Amod Agashé Kristin Lauter Ramarathnam Venkatesan	4
+	Advanced Topics in the Arithmetic of Elliptic Curves	1994	Joseph H. Silverman	4
+	Elliptic Functions	1987	Serge Lang	4
+ PDF Chat	Modular Polynomials for Genus 2	2009	Reinier Bröker Kristin Lauter	4
+ PDF Chat	A Rigorous Time Bound for Factoring Integers	1992	H. W. Lenstra Carl Pomerance	4
+	Generating class fields using Shimura reciprocity	1998	Alice Gee Peter Stevenhagen	4
+	Arithmetic Variety of Moduli for Genus Two	1960	Jun-ichi Igusa	4
+ PDF Chat	Examples of genus two CM curves defined over the rationals	1999	Paul van Wamelen	4
+	Compactification of Arithmetic Quotients of Bounded Symmetric Domains	1966	Walter L. Baily Armand Borel	3
+	On the Graded Ring of Theta-Constants	1964	Jun-ichi Igusa	3
+ PDF Chat	Higher-dimensional 3-adic CM construction	2007	Robert Carls David Kohel David Lubicz	3
+	On Siegel modular forms. Part I.	1993	Bernhard Runge	3
+	On the Class-Number of the Corpus <i>P</i> (√−<i>k</i> )	1928	J. E. Littlewood	3
+	Constructing elliptic curves with given group order over large finite fields	1994	Georg-Johann Lay Horst G. Zimmer	3
+	The moduli space of curves of genus two covering elliptic curves	1994	Naoki Murabayashi	3
+	The number of curves of genus two with elliptic differentials.	1997	Ernst Kani	3
+ PDF Chat	Factoring Integers with Elliptic Curves	1987	H. W. Lenstra	3
+ PDF Chat	Explicit bounds for primality testing and related problems	1990	Eric Bach	3
+ PDF Chat	Computing Igusa class polynomials	2013	Marco Streng	3
+	Elliptic Curves with a Given Number of Points	2004	Reinier Bröker Peter Stevenhagen	3
+ PDF Chat	Modular equations for hyperelliptic curves	2004	Pierrick Gaudry Éric Schost	3
+ PDF Chat	An introduction to the theory of numbers	1960	G. H. Hardy	3
+ PDF Chat	Elliptic curves and primality proving	1993	A. O. L. Atkin François Morain	3
+ PDF Chat	The Difference Between Consecutive Primes, II	2001	Roger C. Baker G. Harman J. Pintz	3
+	On the geometry of a Siegel modular threefold	1982	Gerard van der Geer	3
+	Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology	2001	Kiran S. Kedlaya	3
+ PDF Chat	Modular curves of composite level	2005	Andreas Enge Reinhard Schertz	3
+ PDF Chat	Curves of genus 2 with split Jacobian	1988	Robert Michael Kuhn	3