Let C be a Q-curve with no complex multiplication. In this note we characterize the number fields K such that there is a curve C′ isogenous to C having all the isogenies between its Galois conjugates defined over K, and also the curves C′ isogenous to C defined over a number field K such that the abelian variety ResK/Q(C/K) obtained by restriction of scalars is a product of abelian varieties of...

We give a characterization of the Deligne-Lusztig curve associated to the Suzuki group Sz(q) based on the genus and the number of Fq-rational points of the curve. §0. Throughout this paper by a curve we mean a projective, geometrically irreducible, and non-singular algebraic curve defined over the finite field Fq with q elements. Let Nq(g) denote the maximum number of Fq-rational points that a ...

one of the most problems that limits use of turbomachines at high speed applications is cavitation. cavitation can damage casing and blades of turbopump, also can make unstability in system. inducer that was installed in front of main impeller can improve cavitation characteristic of system and increase static pressure just before entrance of centrifugal pump. specially in fuel feed system of l...

In this paper p, p1, q are points of E 2 T . The following three propositions are true: (1) Let P be a compact non empty subset of E T . Suppose P is a simple closed curve. Then W-minP ∈ LowerArcP and E-maxP ∈ LowerArcP and W-minP ∈ UpperArcP and E-maxP ∈ UpperArcP. (2) For every compact non empty subset P of E T and for every q such that P is a simple closed curve and LE(q,W-minP, P ) holds q ...

We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here, we let both q and m vary; our estimate is explicit and does not depend on the elliptic curve.

Let $E/\mathbb Q(t)$ be an elliptic curve and let $t_0 \in \mathbb Q$ a rational number for which the specialization $E_{t_0}$ is curve. In 2015, Gusić Tadić gave easy-to-check criterion, based only on Weierstrass equation $E/\

We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here we let both q and m vary and our estimate is explicit and does not depend on the elliptic curve.

We study the question of whether algebraic curves of a given genus g defined over a field K must have points rational over the maximal abelian extension K of K. We give: (i) an explicit family of diagonal plane cubic curves without Q-points, (ii) for every number field K, a genus one curve C/Q with no K -points, and (iii) for every g ≥ 4 an algebraic curve C/Q of genus g with no Q-points. In an...

In this article, for any fixed genus g ≥ 1, we prove that a positive proportion of hyperelliptic curves over Q of genus g have points over R and over Qp for all p, but have no points globally over any extension of Q of odd degree. By a hyperelliptic curve over Q, we mean a smooth, geometrically irreducible, complete curve C over Q equipped with a fixed map of degree 2 to P defined over Q. Thus ...