The genus g of an Fq2-maximal curve satisfies g = g1 := q(q − 1)/2 or g ≤ g2 := ⌊(q − 1) /4⌊. Previously, Fq2 -maximal curves with g = g1 or g = g2, q odd, have been characterized up to Fq2 -isomorphism. Here it is shown that an Fq2 -maximal curve with genus g2, q even, is Fq2 -isomorphic to the nonsingular model of the plane curve ∑t i=1 y q/2 = x, q = 2, provided that q/2 is a Weierstrass non...

By reformulating and extending results of Elkies, we prove some on \({{\mathbb {Q}}}\)-curves over number fields odd degree. We show that, such fields, the only prime isogeny degrees \(\ell \) that a {Q}}}\)-curve without CM may have are those already possible {Q}}}\) itself (in particular, \le 37\)), existence bound cyclic isogenies between depending degree field. also torsion groups not divis...

‎By the Mordell‎- ‎Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves‎, ‎where p and q are distinct primes‎. ‎We give infinite families of elliptic curves of the form y2=x3-pqx with rank two‎, ‎three and four‎, ‎assuming a conjecture of Schinzel ...

A Q-curve is an elliptic curve defined over Q that is isogenous to all its Galois conjugates. The term Q-curve was first used by Gross to denote a special class of elliptic curves with complex multiplication having that property, and later generalized by Ribet to denote any elliptic curve isogenous to its conjugates. In this paper we deal only with Q-curves with no complex multiplication, the c...

It is well known that the Gauss map for a complex plane curve birational, whereas in positive characteristic not always birational. Let $q$ be power of prime integer. We study certain degree $q^2 + q 1$ which inseparable with $q$. As special case, we show relation between dual Fermat and Ballico-Hefez curve.

Let be m ∈ Z>0 and a, q ∈ Q. Denote by APm(a, q) the set of rational numbers d such that a, a + q, . . . , a + (m − 1)q form an arithmetic progression in the Edwards curve Ed : x2 +y2 = 1+d x2y2. We study the set APm(a, q) and we parametrize it by the rational points of an algebraic curve.

In this paper, we present the exact Hausdorff distance between the offset curve of quadratic Bézier curve and its quadratic GC1 approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic GC1 approximation of the offset curve of a quadratic Bézier curve. 1. Preliminaries Quadratic Bézier curves and their offset curves are widely used in CAD/CAM or Co...

A lattice model of interacting q-oscillators, proposed by V. Bazhanov and S. Sergeev in 2005 is the quantum-mechanical integrable model in 2 + 1 dimensional space-time. Its layer-to-layer transfer matrix is a polynomial of two spectral parameters, it may be regarded in terms of quantum groups both as a sum of sl(N) transfer matrices of a chain of length M and as a sum of sl(M) transfer matrices...