**Contemporary Mathematics**

Volume: 463;
2008;
129 pp;
Softcover

MSC: Primary 14; 11;

Print ISBN: 978-0-8218-4320-8

Product Code: CONM/463

List Price: $53.00

Individual Member Price: $42.40

**Electronic ISBN: 978-0-8218-8142-2
Product Code: CONM/463.E**

List Price: $53.00

Individual Member Price: $42.40

# Computational Arithmetic Geometry

Share this page *Edited by *
*Kristin E. Lauter; Kenneth A. Ribet*

With the recent increase in available computing power, new computations are possible in many areas of arithmetic geometry. To name just a few examples, Cremona's tables of elliptic curves now go up to conductor 120,000 instead of just conductor 1,000, tables of Hilbert class fields are known for discriminant up to at least 5,000, and special values of Hilbert and Siegel modular forms can be calculated to extremely high precision. In many cases, these experimental capabilities have led to new observations and ideas for progress in the field. They have also led to natural algorithmic questions on the feasibility and efficiency of many computations, especially for the purpose of applications in cryptography. The AMS Special Session on Computational Arithmetic Geometry, held on April 29–30, 2006, in San Francisco, CA, gathered together many of the people currently working on the computational and algorithmic aspects of arithmetic geometry. This volume contains research articles related to talks given at the session. The majority of articles are devoted to various aspects of arithmetic geometry, mainly with a computational approach.

#### Table of Contents

# Table of Contents

## Computational Arithmetic Geometry

- Contents vii8 free
- Preface ix10 free
- Schedule of talks xi12 free
- Results of Cohen–Lenstra type for quadratic function fields 114 free
- The hardness of computing an eigenform 922
- Constructing elliptic curves of prime order 1730
- Space-time codes and non-associative division algebras arising from elliptic curves 2942
- Points of low height on P1 over number fields and bounds for torsion in class groups 4558
- Supersingular genus-2 curves over fields of characteristic 3 4962
- Search techniques for root-unitary polynomials 7184
- Yet more elements in the Shafarevich–Tate group of the jacobian of a Fermat Curve 8396
- Stable reduction of X0(81) 91104
- Isomorphism types of commutative algebras of finite rank over an algebraically closed field 111124
- A short guide to p-torsion of abelian varieties in characteristic p 121134

#### Readership

Graduate students and research mathematicians interested in arithmetic geometry and computational number theory.