Michael Stoll

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All published works

Action	Title	Year	Authors
+	Complete verification of strong BSD for many modular abelian surfaces over ${\mathbf {Q}}$	2025	Timo Keller Michael Stoll
+ PDF Chat	Brauer–Manin obstructions requiring arbitrarily many Brauer classes	2024	Jennifer Berg Carlo Pagano Bjorn Poonen Michael Stoll Nicholas Triantafillou Bianca Viray Isabel Vogt
+ PDF Chat	Minimization of hypersurfaces	2023	Andreas-Stephan Elsenhans Michael Stoll
+ PDF Chat	Dynamics of quadratic polynomials and rational points on a curve of genus 4	2023	Hang Fu Michael Stoll
+ PDF Chat	Torsion points on elliptic curves over number fields of small degree	2023	Maarten Derickx S. Kamienny William Stein Michael Stoll
+	The Cassels-Tate pairing on 2-Selmer groups of elliptic curves	2023	Himanshu Shukla Michael Stoll
+	Brauer-Manin obstructions requiring arbitrarily many Brauer classes	2023	Jennifer Berg Carlo Pagano Bjorn Poonen Michael Stoll Nicholas Triantafillou Bianca Viray Isabel Vogt
+	Complete verification of strong BSD for many modular abelian surfaces over $\mathbf{Q}$	2023	Timo Keller Michael Stoll
+ PDF Chat	On strongly walk regular graphs, triple sum sets and their codes	2022	Michael Kiermaier Sascha Kurz Patrick Solé Michael Stoll Alfred Wassermann
+	The Weierstrass–Durand–Kerner root finder is not generally convergent	2022	Bernhard Reinke Dierk Schleicher Michael Stoll
+ PDF Chat	Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces	2022	Timo Keller Michael Stoll
+ PDF Chat	Elliptic curves with common torsion 𝑥-coordinates and hyperelliptic torsion packets	2022	Hang Fu Michael Stoll
+	Dynamics of quadratic polynomials and rational points on a curve of genus $4$	2022	Hang Fu Michael Stoll
+ PDF Chat	Elliptic curves with a point of order $13$ defined over cyclic cubic fields	2021	Peter Bruin Maarten Derickx Michael Stoll
+	Elliptic curves with a point of order 13 defined over cyclic cubic fields.	2021	Peter Bruin Maarten Derickx Michael Stoll
+	Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces	2021	Timo Keller Michael Stoll
+	Elliptic curves with a point of order 13 defined over cyclic cubic fields	2021	Peter C. de Bruin Maarten Derickx Michael Stoll
+	Minimization of hypersurfaces	2021	Andreas-Stephan Elsenhans Michael Stoll
+	The Weierstrass root finder is not generally convergent	2020	Bernhard Reinke Dierk Schleicher Michael Stoll
+	Eventually stable quadratic polynomials over ℚ	2020	David DeMark Wade Hindes Rafe Jones Moses Misplon Michael Stoll Michael Stoneman
+	On strongly walk regular graphs, triple sum sets and their codes	2020	Michael Kiermaier Sascha Kurz Patrick Solé Michael Stoll Alfred Wassermann
+	The Weierstrass root finder is not generally convergent	2020	Bernhard Reinke Dierk Schleicher Michael Stoll
+	Elliptic curves with common torsion $x$-coordinates and hyperelliptic torsion packets	2019	Hang Fu Michael Stoll
+	The generalized Fermat equation with exponents 2, 3,	2019	Nuno Freitas Bartosz Naskręcki Michael Stoll
+	Eventually stable quadratic polynomials over $\mathbb{Q}$	2019	David DeMark Wade Hindes Rafe Jones Moses Misplon Michael Stoll Michael Stoneman
+ PDF Chat	Irreducibility of polynomials with a large gap	2019	Will Sawin Mark Shusterman Michael Stoll
+	An application of "Selmer group Chabauty" to arithmetic dynamics	2019	Michael Stoll
+ PDF Chat	Diagonal genus 5 curves, elliptic curves over $\mathbb {Q}(t)$, and rational diophantine quintuples	2019	Michael Stoll
+ PDF Chat	Smallest representatives of $\rm {SL}(2,\mathbb {Z})$-orbits of binary forms and endomorphisms of $\mathbb {P}^1$	2019	Benjamin Hutz Michael Stoll
+	Eventually stable quadratic polynomials over $\mathbb{Q}$	2019	David DeMark Wade Hindes Rafe Jones Moses Misplon Michael Stoll Michael R. Stoneman
+ PDF Chat	Uniform bounds for the number of rational points on hyperelliptic curves of small Mordell–Weil rank	2018	Michael Stoll
+	Irreducibility of polynomials with a large gap.	2018	William F. Sawin Mark Shusterman Michael Stoll
+	Computeralgebra	2018	Sascha Kurz Michael Stoll Karl Worthmann
+	Irreducibility of polynomials with a large gap	2018	William F. Sawin Mark Shusterman Michael Stoll
+	Quadratic rational functions with a rational periodic critical point of period 3	2017	Solomon Vishkautsan Michael Stoll
+ PDF Chat	Geometry and arithmetic of primary Burniat surfaces	2017	Ingrid Bauer Michael Stoll
+	Chabauty Without the Mordell-Weil Group	2017	Michael Stoll
+	An Explicit Theory of Heights for Hyperelliptic Jacobians of Genus Three	2017	Michael Stoll
+	The generalized Fermat equation with exponents 2, 3, n	2017	Nuno Freitas Bartosz Naskręcki Michael Stoll
+	Torsion points on elliptic curves over number fields of small degree	2017	Maarten Derickx S. Kamienny William E. Stein Michael Stoll
+	Quadratic rational functions with a rational periodic critical point of period 3	2017	Solomon Vishkautsan Michael Stoll
+ PDF Chat	Canonical heights on genus-2 Jacobians	2016	J. Steffen Müller Michael Stoll
+ PDF Chat	Simultaneous Torsion in the Legendre Family	2016	Michael Stoll
+	GENERALIZED EXPLICIT DESCENT AND ITS APPLICATION TO CURVES OF GENUS 3	2016	Nils Bruin Bjorn Poonen Michael Stoll
+ PDF Chat	Computing canonical heights on elliptic curves in quasi-linear time	2016	J. Steffen Müller Michael Stoll
+	p-adic Analysis in Arithmetic Geometry	2016	Michael Stoll
+ PDF Chat	GENERALIZED EXPLICIT DESCENT AND ITS APPLICATION TO CURVES OF GENUS 3	2016	Nils Bruin Bjorn Poonen Michael Stoll
+	Rational points on primary Burniat surfaces	2015	Ingrid Bauer Michael Stoll
+	Descent and covering collections	2015	Michael Stoll
+ PDF Chat	Explicit $n$-descent on elliptic curves III. Algorithms	2014	J. E. Cremona Tom Fisher Cathy O'Neil Denis Simon Michael Stoll
+ PDF Chat	Most odd degree hyperelliptic curves have only one rational point	2014	Bjorn Poonen Michael Stoll
+ PDF Chat	The generalised Fermat equation x 2 + y 3 = z 15	2014	Samir Siksek Michael Stoll
+	Rational points on hyperelliptic curves : recent developments	2014	Michael Stoll
+ PDF Chat	On elliptic curves with an isogeny of degree 7	2014	Ralph Greenberg Karl Rubin Alice Silverberg Michael Stoll
+	Uniform bounds for the number of rational points on hyperelliptic curves of small Mordell-Weil rank	2013	Michael Stoll
+	CHABAUTY'S METHOD PROVES THAT MOST ODD DEGREE HYPERELLIPTIC CURVES HAVE ONLY ONE RATIONAL POINT	2013	Bjorn Poonen Michael Stoll
+ PDF Chat	Explicit Selmer groups for cyclic covers of P<sup>1</sup>	2013	Michael Stoll Ronald van Luijk
+	Uniform bounds for the number of rational points on hyperelliptic curves of small Mordell-Weil rank	2013	Michael Stoll
+	Wie man Diophantische Gleichungen löst	2012	Michael Stoll
+ PDF Chat	Explicit isogeny descent on elliptic curves	2012	Robert Miller Michael Stoll
+	Arbeitsgruppe Algorithmische Arithmetische Geometrie an der Universität Bayreuth	2012	Michael Stoll
+	Explicit methods in number theory. Rational points and Diophantine equations.	2012	Karim Belabas Frits Beukers Pierrick Gaudry William G. McCallum Bjorn Poonen Samir Siksek Michael Stoll Mark E. Watkins
+ PDF Chat	Partial descent on hyperelliptic curves and the generalized Fermat equation <i>x</i> <sup>3</sup> +<i>y</i> <sup>4</sup> +<i>z</i> <sup>5</sup> =0	2011	Samir Siksek Michael Stoll
+	Unfaking the fake Selmer group	2011	Michael Stoll Ronald van Luijk
+ PDF Chat	ON THE NUMBER OF RATIONAL ITERATED PREIMAGES OF THE ORIGIN UNDER QUADRATIC DYNAMICAL SYSTEMS	2011	Xander Faber Benjamin Hutz Michael Stoll
+ PDF Chat	Reduction theory of point clusters in projective space	2011	Michael Stoll
+	Stability of peak solutions of a non-linear transport equation on the circle	2011	Edith Geigant Michael Stoll
+	How to Solve a Diophantine Equation	2011	Michael Stoll
+ PDF Chat	Rational points on curves	2011	Michael Stoll
+ PDF Chat	The yoga of the Cassels–Tate pairing	2010	Tom Fisher Edward F. Schaefer Michael Stoll
+ PDF Chat	Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves	2010	J. E. Cremona Tom Fisher Michael Stoll
+ PDF Chat	The Mordell–Weil sieve: proving non-existence of rational points on curves	2010	Nils Bruin Michael Stoll
+	Rational points on curves	2010	Michael Stoll
+ PDF Chat	On a Problem of Hajdu and Tengely	2010	Samir Siksek Michael Stoll
+	On elliptic curves with an isogeny of degree 7	2010	Ralph Greenberg Karl Rubin Alice Silverberg Michael Stoll
+	Explicit isogeny descent on elliptic curves	2010	Robert Miller Michael Stoll
+	How to Solve a Diophantine Equation	2010	Michael Stoll
+	On a problem of Hajdu and Tengely	2009	Samir Siksek Michael Stoll
+	Reduction theory of point clusters in projective space	2009	Michael Stoll
+	Rational Points on Curves of Genus 2 : Experiments and Speculations	2009	Michael Stoll
+ PDF Chat	Two-cover descent on hyperelliptic curves	2009	Nils Bruin Michael Stoll
+	On the average number of rational points on curves of genus 2	2009	Michael Stoll
+ PDF Chat	On the Diophantine equation X<sup>2</sup>-(2<sup>2m</sup>+1)Y<sup>4</sup>=-2<sup>2m</sup>	2009	Michael Stoll Peter Walsh Pingzhi Yuan
+ PDF Chat	Explicit n-descent on elliptic curves, II. Geometry	2009	J. E. Cremona Tom Fisher Caroline A. O’Neil Denis Simon Michael Stoll
+	Reduction theory of point clusters in projective space	2009	Michael Stoll
+	On a problem of Hajdu and Tengely	2009	Samir Siksek Michael Stoll
+ PDF Chat	Integral points on hyperelliptic curves	2008	Yann Bugeaud Maurice Mignotte Samir Siksek Michael Stoll Szabolcs Tengely
+	On the Number of Rational Iterated Pre-images of the Origin Under Quadratic Dynamical Systems	2008	Xander Faber Benjamin Hutz Michael Stoll
+	Rational 6-cycles under iteration of quadratic polynomials	2008	Michael Stoll
+ PDF Chat	Deciding Existence of Rational Points on Curves: An Experiment	2008	Nils Bruin Michael Stoll
+ PDF Chat	Explicit n-descent on elliptic curves, I. Algebra	2008	J. E. Cremona Tom Fisher Cathy O'Neil Denis Simon Michael Stoll
+	Integral Points on Hyperelliptic Curves	2008	Yann Bugeaud Max Mignotte Samir Siksek Michael Stoll Sz. Tengely
+ PDF Chat	Rational 6-Cycles Under Iteration of Quadratic Polynomials	2008	Michael Stoll
+	Documentation for the ratpoints program	2008	Michael Stoll
+	On the Number of Rational Iterated Pre-images of the Origin Under Quadratic Dynamical Systems	2008	Xander Faber Benjamin Hutz Michael Stoll
+ PDF Chat	Finite descent obstructions and rational points on curves	2007	Michael Stoll
+ PDF Chat	Twists of X(7) and primitive solutions to x2+y3=z7	2007	Bjorn Poonen Edward F. Schaefer Michael Stoll
+ PDF Chat	Independence of rational points on twists of a given curve	2006	Michael Stoll
+	Finite descent and rational points on curves	2006	Michael Stoll
+	Finite descent obstructions and rational points on curves	2006	Michael Stoll
+	Descent on elliptic curves	2006	Michael Stoll
+	Deciding existence of rational points on curves: an experiment	2006	Nils Bruin Michael Stoll
+ PDF Chat	On the number of rational squares at fixed distance from a fifth power	2006	Michael Stoll
+	Finite descent obstructions and rational points on curves	2006	Michael Stoll
+	An Introduction to Conway's Games and Numbers	2004	Dierk Schleicher Michael Stoll
+	How to do a 𝑝-descent on an elliptic curve	2003	Edward F. Schaefer Michael Stoll
+	ON THE L-FUNCTION OF THE CURVES $\lowercase{y}^2 = \lowercase{x}^5 + A$	2003	Michael Stoll Tonghai Yang
+	Bifurcation analysis of an orientational aggregation model	2003	Edith Geigant Michael Stoll
+ PDF Chat	On the reduction theory of binary forms	2003	Michael Stoll J. E. Cremona
+	On the Arithmetic of the Curves y2=xℓ+A, II	2002	Michael Stoll
+ PDF Chat	On the height constant for curves of genus two, II	2002	Michael Stoll
+ PDF Chat	Minimal Models for 2-coverings of Elliptic Curves	2002	Michael Stoll J. E. Cremona
+	Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves	2001	E. V. Flynn Franck Leprévost Edward F. Schaefer William Stein Michael Stoll Joseph L. Wetherell
+ PDF Chat	Implementing 2-descent for Jacobians of hyperelliptic curves	2001	Michael Stoll
+ PDF Chat	The Cassels-Tate Pairing on Polarized Abelian Varieties	1999	Bjorn Poonen Michael Stoll
+	A Local-Global Principle for Densities	1999	Bjorn Poonen Michael Stoll
+ PDF Chat	On the height constant for curves of genus two	1999	Michael Stoll
+	On the arithmetic of the curves o y2 = xℓ + A and their Jacobians	1998	Michael Stoll
+	Rational and transcendental growth series for the higher Heisenberg groups	1996	Michael Stoll
+ PDF Chat	Construction of semiabelian Galois extensions	1995	Michael Stoll
+	Two simple 2-dimensional abelian varieties defined over Q with Mordell-Weil group of rank at least 19	1995	Michael Stoll
+	Asymptotics of some number theoretic functions and an application to the growth of nilpotent groups	1994	Michael Stoll
+	Galois groups over $$cQ$$ of some iterated polynomials	1992	Michael Stoll

Common Coauthors

Coauthor	Papers Together
Bjorn Poonen	10
Samir Siksek	8
Nils Bruin	6
J. E. Cremona	6
Maarten Derickx	5
Tom Fisher	5
Dierk Schleicher	4
Edward F. Schaefer	4
Benjamin Hutz	4
Timo Keller	4
Xander Faber	3
Hang Fu	3
Sascha Kurz	3
Wade Hindes	3
Bernhard Reinke	3
David DeMark	3
Denis Simon	3
Mark Shusterman	3
Alfred Wassermann	2
Carlo Pagano	2
Robert Miller	2
Ralph Greenberg	2
Nuno Freitas	2
Bartosz Naskręcki	2
Patrick Solé	2
Rafe Jones	2
Alice Silverberg	2
Edith Geigant	2
Moses Misplon	2
Solomon Vishkautsan	2
Jennifer Berg	2
Michael Stoneman	2
Andreas-Stephan Elsenhans	2
Cathy O'Neil	2
Isabel Vogt	2
Michael Kiermaier	2
Bianca Viray	2
Nicholas Triantafillou	2
S. Kamienny	2
William Stein	2
Karl Rubin	2
Peter Bruin	2
Ronald van Luijk	2
Yann Bugeaud	2
Ingrid Bauer	2
J. Steffen Müller	2
William F. Sawin	2
Peter C. de Bruin	1
Szabolcs Tengely	1
Mark E. Watkins	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	The Magma Algebra System I: The User Language	1997	Wieb Bosma John Cannon Catherine Playoust	48
+ PDF Chat	Implementing 2-descent for Jacobians of hyperelliptic curves	2001	Michael Stoll	30
+ PDF Chat	The Mordell–Weil sieve: proving non-existence of rational points on curves	2010	Nils Bruin Michael Stoll	23
+ PDF Chat	Independence of rational points on twists of a given curve	2006	Michael Stoll	22
+ PDF Chat	Two-cover descent on hyperelliptic curves	2009	Nils Bruin Michael Stoll	19
+ PDF Chat	On the height constant for curves of genus two, II	2002	Michael Stoll	15
+	EXPLICIT DESCENT FOR JACOBIANS OF CYCLIC COVERS OF THE PROJECTIVE LINE	1997	Bjorn Poonen Edward F. Schaefer	15
+ PDF Chat	The Arithmetic of Elliptic Curves	1986	Joseph H. Silverman	14
+	Algorithms for Modular Elliptic Curves	1992	J. E. Cremona	14
+ PDF Chat	Twists of X(7) and primitive solutions to x2+y3=z7	2007	Bjorn Poonen Edward F. Schaefer Michael Stoll	13
+ PDF Chat	Heuristics for the Brauer–Manin Obstruction for Curves	2006	Bjorn Poonen	12
+	Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves	2001	E. V. Flynn Franck Leprévost Edward F. Schaefer William Stein Michael Stoll Joseph L. Wetherell	12
+	Explicit descent for Jacobians of cyclic coevers of the projective line.	1997		12
+	Endlichkeitss�tze f�r abelsche Variet�ten �ber Zahlk�rpern	1983	Герд Фалтингс	12
+ PDF Chat	Computing a Selmer group of a Jacobian using functions on the curve	1998	Edward F. Schaefer	12
+	Chabauty methods using elliptic curves	2003	Nils Bruin	12
+	How to do a 𝑝-descent on an elliptic curve	2003	Edward F. Schaefer Michael Stoll	12
+	Advanced Topics in the Arithmetic of Elliptic Curves	1994	Joseph H. Silverman	11
+	Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2	1996	J. W. S. Cassels E. V. Flynn	11
+ PDF Chat	Finite descent obstructions and rational points on curves	2007	Michael Stoll	11
+ PDF Chat	Deciding Existence of Rational Points on Curves: An Experiment	2008	Nils Bruin Michael Stoll	11
+	Arithmetic Duality Theorems	1987	J. S. Milne	11
+ PDF Chat	On the height constant for curves of genus two	1999	Michael Stoll	10
+ PDF Chat	The Cassels-Tate Pairing on Polarized Abelian Varieties	1999	Bjorn Poonen Michael Stoll	10
+ PDF Chat	Canonical heights on the Jacobians of curves of genus 2 and the infinite descent	1997	E. V. Flynn Nigel P. Smart	10
+ PDF Chat	The Hasse principle and the Brauer-Manin obstruction for curves	2004	E. V. Flynn	10
+	Modular Elliptic Curves and Fermat's Last Theorem	1995	Andrew Wiles	10
+	The Arithmetic of Elliptic Curves	2009	Joseph H. Silverman	9
+ PDF Chat	Computing Special Values of Motivic<i>L</i>-Functions	2004	Tim Dokchitser	9
+ PDF Chat	Cycles of quadratic polynomials and rational points on a genus-2 curve	1997	E. V. Flynn Bjorn Poonen Edward F. Schaefer	9
+ PDF Chat	Rational 6-Cycles Under Iteration of Quadratic Polynomials	2008	Michael Stoll	9
+	On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises	2001	Christophe Breuil Brian Conrad Fred Diamond Richard Taylor	9
+	Ring-Theoretic Properties of Certain Hecke Algebras	1995	Richard Taylor Andrew Wiles	8
+	Explicit 8-descent on elliptic curves	2005	Sebastian Karl Michael Stamminger	8
+	Néron Models	1990	Siegfried Bosch Werner Lütkebohmert Michel Raynaud	7
+	2-Descent on the Jacobians of Hyperelliptic Curves	1995	Edward F. Schaefer	7
+	Local -global problems and the Brauer -Manin obstruction.	1999	Victor Scharaschkin	7
+	Chabauty methods and covering techniques applied to generalized Fermat equations	2002	Nils Bruin	7
+ PDF Chat	Towers of 2-covers of hyperelliptic curves	2005	Nils Bruin E. V. Flynn	6
+ PDF Chat	Explicit n-descent on elliptic curves, I. Algebra	2008	J. E. Cremona Tom Fisher Cathy O'Neil Denis Simon Michael Stoll	6
+ PDF Chat	Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves	2010	J. E. Cremona Tom Fisher Michael Stoll	6
+	Bounding the number of rational points on certain curves of high rank	2001	Joseph L. Wetherell	6
+	Rational isogenies of prime degree	1978	Barry Mazur Dorian Goldfeld	6
+ PDF Chat	Finding rational points on bielliptic genus 2 curves	1999	E. V. Flynn Joseph L. Wetherell	6
+ PDF Chat	Explicit 4-descents on an elliptic curve	1996	J. R. Merriman Samir Siksek Nigel P. Smart	6
+	Class Groups and Selmer Groups	1996	Edward F. Schaefer	6
+ PDF Chat	Modular curves and the eisenstein ideal	1977	Barry Mazur	6
+	A Local-Global Principle for Densities	1999	Bjorn Poonen Michael Stoll	6
+	Second isogeny descents and the Birch and Swinnerton-Dyer conjectural formula	2012	Brendan Creutz Robert Miller	5
+	Second descents for elliptic curves	1998	J. W. S. Cassels	5