Vol. 1, No. 1, 2013

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Recent Volumes
1: ANTS X
The Open Book Series
About the Series
Ethics Statement
Preface
7–9

Everett W. Howe and Kiran S. Kedlaya

Deterministic elliptic curve primality proving for a special sequence of numbers
1–20

Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland and Angela Wong

Imaginary quadratic fields with isomorphic abelian Galois groups
21–39

Athanasios Angelakis and Peter Stevenhagen

Iterated Coleman integration for hyperelliptic curves
41–61

Jennifer S. Balakrishnan

Finding ECM-friendly curves through a study of Galois properties
63–86

Razvan Barbulescu, Joppe W. Bos, Cyril Bouvier, Thorsten Kleinjung and Peter L. Montgomery

Two grumpy giants and a baby
87–111

Daniel J. Bernstein and Tanja Lange

Improved techniques for computing the ideal class group and a system of fundamental units in number fields
113–133

Jean-François Biasse and Claus Fieker

Conditionally bounding analytic ranks of elliptic curves
135–144

Jonathan W. Bober

A database of elliptic curves over ${\mathbb Q}(\sqrt{5})$: a first report
145–166

Jonathan Bober, Alyson Deines, Ariah Klages-Mundt, Benjamin LeVeque, R. Andrew Ohana, Ashwath Rabindranath, Paul Sharaba and William Stein

Finding simultaneous Diophantine approximations with prescribed quality
167–185

Wieb Bosma and Ionica Smeets

Success and challenges in determining the rational points on curves
187–212

Nils Bruin

Solving quadratic equations in dimension $5$ or more without factoring
213–233

Pierre Castel

Counting value sets: algorithm and complexity
235–248

Qi Cheng, Joshua E. Hill and Daqing Wan

Haberland's formula and numerical computation of Petersson scalar products
249–270

Henri Cohen

Approximate common divisors via lattices
271–293

Henry Cohn and Nadia Heninger

Explicit descent in the Picard group of a cyclic cover of the projective line
295–315

Brendan Creutz

Computing equations of curves with many points
317–334

Virgile Ducet and Claus Fieker

Computing the unit group, class group, and compact representations in algebraic function fields
335–358

Kirsten Eisenträger and Sean Hallgren

The complex polynomials $P(x)$ with $\mathop{\rm Gal}(P(x)-t) \cong M_{23}$
359–367

Noam D. Elkies

Experiments with the transcendental Brauer-Manin obstruction
369–394

Andreas-Stephan Elsenhans and Jörg Jahnel

Explicit $5$-descent on elliptic curves
395–411

Tom Fisher

On the density of abelian surfaces with Tate-Shafarevich group of order five times a square
413–435

Stefan Keil and Remke Kloosterman

Improved CRT algorithm for class polynomials in genus $2$
437–461

Kristin E. Lauter and Damien Robert

Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent
463–486

Reynald Lercier, Christophe Ritzenthaler and Jeroen Sijsling

Elliptic factors in Jacobians of hyperelliptic curves with certain automorphism groups
487–505

Jennifer Paulhus

Isogeny volcanoes
507–530

Andrew V. Sutherland

On the evaluation of modular polynomials
531–555

Andrew V. Sutherland

Constructing and tabulating dihedral function fields
557–585

Colin Weir, Renate Scheidler and Everett W. Howe