Explicit points on the Legendre curve III
نویسنده
چکیده
منابع مشابه
Explicit points on the Legendre curve
We study the elliptic curve E given by y = x(x+1)(x+ t) over the rational function field k(t) and its extensions Kd = k(μd, t). When k is finite of characteristic p and d = p + 1, we write down explicit points onE and show by elementary arguments that they generate a subgroup Vd of rank d − 2 and of finite index in E(Kd). Using more sophisticated methods, we then show that the Birch and Swinner...
متن کاملLegendre elliptic curves over finite fields
Throughout this paper, q > 1 denotes a power of an odd prime number p, and k is a field. Given two elliptic curves E/k and E′/k, all morphisms from E to E′ are understood to be defined over k. In particular, we simply write End(E) for the ring of all endomorphisms of E/k. The notation E ≃ E′ indicates that E is isomorphic to E′, and E ∼ E′ means that E and E′ are isogenous. The endomorphism of ...
متن کاملError Analysis for Mapped Legendre Spectral and Pseudospectral Methods
A general framework is introduced to analyze the approximation properties of mapped Legendre polynomials and of interpolations based on mapped Legendre–Gauss–Lobatto points. Optimal error estimates featuring explicit expressions on the mapping parameters for several popular mappings are derived. These results not only play an important role in numerical analysis of mapped Legendre spectral and ...
متن کاملCurves of Genus 2 with Split Jacobian
We say that an algebraic curve has split jacobian if its jacobian is isogenous to a product of elliptic curves. If X is a curve of genus 2, and /: X —► E a map from X to an elliptic curve, then X has split jacobian. It is not true that a complement to E in the jacobian of X is uniquely determined, but, under certain conditions, there is a canonical choice of elliptic curve E' and algebraic f:X—...
متن کاملA Novel Family of Mathematical Self-calibration Additional Parameters for Airborne Camera Systems
Self-calibration additional parameters (APs) have identified their significant role in photogrammetric calibration and orientation since 1970s. However, the traditional APs might not be adequate for the digital airborne camera calibration. A novel family of mathematical self-calibration APs is presented in this paper. We point out that photogrammetric self-calibration can, to a very large exten...
متن کامل