Invited papers -- Putting the Hodge and Tate Conjectures to the Test -- Curves of Genus 3 with a Group of Automorphisms Isomorphic to S3 -- Learning with Errors over Rings -- Lattices and Spherical Designs -- Fixed Points for Discrete Logarithms -- Contributed papers -- Explicit Coleman Integration for Hyperelliptic Curves -- Smallest Reduction Matrix of Binary Quadratic Forms -- Practical Improvements to Class Group and Regulator Computation of Real Quadratic Fields -- On the Use of the Negation Map in the Pollard Rho Method -- An O(M(n) logn) Algorithm for the Jacobi Symbol -- New Families of ECM Curves for Cunningham Numbers -- Visualizing Elements of Sha[3] in Genus 2 Jacobians -- On Weil Polynomials of K3 Surfaces -- Class Invariants by the CRT Method -- Short Bases of Lattices over Number Fields -- On the Complexity of the Montes Ideal Factorization Algorithm -- Congruent Number Theta Coefficients to 1012 -- Pairing the Volcano -- A Subexponential Algorithm for Evaluating Large Degree Isogenies -- Huff’s Model for Elliptic Curves -- Efficient Pairing Computation with Theta Functions -- Small-Span Characteristic Polynomials of Integer Symmetric Matrices -- Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field -- Factoring Polynomials over Local Fields II -- On a Problem of Hajdu and Tengely -- Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures -- On the Extremality of an 80-Dimensional Lattice -- Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number -- Improved Primality Proving with Eisenstein Pseudocubes -- Hyperbolic Tessellations Associated to Bianchi Groups.