Related papers: Efficiently computable endomorphisms for hyperelli…

The classical theory of elliptic curves with complex multiplication is a fundamental tool for studying the arithmetic of abelian extensions of imaginary quadratic fields. While no direct analogue is available for real quadratic fields, a…

We list the elliptic curves defined over $Q(\sqrt 5)$ with good reduction away from 2. There are 368 isomorphism classes. We give a global minimal model for each class.

We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions…

Current monolithic quantum computer architectures have limited scalability. One promising approach for scaling them up is to use a modular or multi-core architecture, in which different quantum processors (cores) are connected via quantum…

The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that…

This paper presents a generalization of a method allowing the transformation of the Elliptic Curve Discrete Logarithm Problem (ECDLP) over prime fields to the Quadratic Unconstrained Binary Optimization (QUBO) problem. The original method…

We solve the problem of counting elliptic curves with fixed j-invariant in projective space with tangency conditions. This is equivalent to couting rational nodal curves with condition on the node of the image. The solution is given in the…

An abelian variety admits only a finite number of isomorphism classes of principal polarizations. The paper gives an interpretation of this number in terms of class numbers of definite Hermitian forms in the case of a product of elliptic…

This survey focuses on the computational complexity of some of the fundamental decision problems in 3-manifold theory. The article discusses the wide variety of tools that are used to tackle these problems, including normal and almost…

We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…

The study of alternative models for elliptic curves has found recent interest from cryptographic applications, once it was recognized that such models provide more efficiently computable algorithms for the group law than the standard…

We investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular $j$-invariants. By analyzing quadratic points on some modular curves, we show that all elliptic…

We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.

We show that there are infinitely many elliptic curves $E/\mathbb{Q}$, up to isomorphism over $\overline{\mathbb{Q}}$, for which the finitely generated group $E(\mathbb{Q})$ has rank exactly $2$. Our elliptic curves are given by explicit…

We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…

In this paper we construct parameterizations of elliptic curves over the rationals which have many consecutive integral multiples. Using these parameterizations, we perform searches in GMP and Magma to find curves with points of small…

Let O be a maximal order in the quaternion algebra B_p over Q ramified at p and infinity. The paper is about the computational problem: Construct a supersingular elliptic curve E over F_p such that End(E) = O. We present an algorithm that…

We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…

Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant way of representing finite field extensions. A natural question which seems to have been considered independently by several groups is to use this representation…

This paper studies the notion of computational entropy. Using techniques from convex optimization, we investigate the following problems: (a) Can we derandomize the computational entropy? More precisely, for the computational entropy, what…