Maximal hyperelliptic curves of genus three
WebFirst assume that HyperellipticPolynomial (A) has odd degree. The function HomologyBasis (A) returns three values which we label basepoints, loops and S. Then basepoints is a list of points in the complex plane. The return value loops is … Webmaximal genus 3 curves (we will recall some here), but a general con-venient method that for given pprime constructs one such curve over F p2 seems unknown. Here are some examples; see [4]. The Dyck-Fermat curve given by x 4+ y + z4 = 0 is maximal over F p2, for every prime number p 3 mod 4. The hyperelliptic curve corresponding to y2 = x7+1 …
Maximal hyperelliptic curves of genus three
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WebConstructing genus 3 hyperelliptic Jacobians with CM Jennifer S. Balakrishnan, Sorina Ionica, Kristin Lauter, and Christelle Vincent Abstract Given a sextic CM eld K, we give an explicit method for nding all genus 3 hyperelliptic curves de ned over C whose … Web1 תשע"ו,כא בתשרי A abbreviate )ְמקַ צֵּ ר (פִ ע Abel )אַ בֵּּ ל (שם פרטי Abel summation סְ כִ ימַ ת אַ בֵּּ ל abelian )אַ בֵּּ לִ י (ת abelian category קָ טֵּ גו ְֹריָה אַ בֵּּ לִ ית abelian extension הַ ְרחָ בָ ה אַ בֵּּ לִ ית abelian group ...
http://waifi.org/documents/AcceptedPapers2024/T2-WAIFI_2024_paper_15.pdf WebIn this paper, we study a Howe curve C C in positive characteristic p≥ 3 p ≥ 3 which is of genus 3 and is hyperelliptic. We will show that if C C is superspecial, then its standard form is maximal or minimal over Fp2 F p 2 without taking its Fp2 F p 2 -form. …
WebKeywords: Cryptosystem; hyperelliptic curves; injective encoding; finite field. 1. Introduction We first recall that a hyperelliptic curve H of gunes g is a curve by the equation y 2 = f (x), where f a squarefree, monic polynomial of degree 2g + 1. Every hyper- elliptic curve of genus 1 is called an elliptic curve. WebMaximal hyperelliptic curves of genus three. EN. English Deutsch Français Español Português Italiano Român Nederlands Latina Dansk Svenska Norsk Magyar Bahasa Indonesia Türkçe Suomi Latvian Lithuanian česk ...
WebLet Cbe a curve of genus 2 and ψ1: C−→ E1 a map of degree n, from Cto an elliptic curve E1, both curves defined over C. This map induces a degree nmap φ1: P1 −→ P1 which we call a Frey-Kani covering. We determine all possible ramifications for φ1. If ψ1: C−→ E1 is maximal then there exists a maximal map ψ2: C−→ E2, of ...
WebEncoding to hyperelliptic curves Ulas [16] simplified and generalized the proposed method by Shallu and Woestijne [14] to encode Fq to hyperelliptic curves of the forms y 2 = xn + ax + b and y 2 = Embedding Finite Fields into Elliptic Curves 899 xn + ax2 + bx. Foque and Tibouchi [10] proposed a deterministic encoding in to hyperelliptic curves of the form y … psychiatry liability insuranceWebThe article was published on 2008-01-01 and is currently open access. It has received 35 citation(s) till now. The article focuses on the topic(s): Arithmetic zeta function & Riemann zeta function. hospital andrews texasWebThe two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real part of √z. The imaginary part of √zis represented by the coloration of the points. For this function, it is also the height after rotating the … hospital and unit cost allocation methodsWebHYPERELLIPTIC CURVES over k of this form. This subtlety does not arise when working overfinitefields (to show this, combine Theorem 10.7.4 with the Riemann-Roch theorem), hence we will define hyperelliptic curves using a generalisation of the Weierstrass equation. The genus has already been defined (see Definition 8.4.8) as a measure of ... hospital anderson houston texasWebKeywords: Cryptosystem; hyperelliptic curves; injective encoding; finite field. 1. Introduction We first recall that a hyperelliptic curve H of gunes g is a curve by the equation y 2 = f (x), where f a squarefree, monic polynomial of degree 2g + 1. Every … psychiatry license californiaWebIt is clear that the curve is A 1-stable hyperelliptic of genus 2m+ 1 and its geometric quotient has 2mcomponents. The odd case can be dealt similarly. Lemma2.1assures us that the geometric quotient Zhas at most two irreducible components if Chas genus 3 and does not have separating nodes. Therefore, the datum (Z=S;L;i) is in the 8 hospital and surgicalWebEquivalent curves on surfaces - Binbin XU 徐彬斌, Nankai (2024-12-20) We consider a closed oriented surface of genus at least 2. To describe curves on it, one natural idea is to choose once for all a collection of curves as a reference system and to hope that any other curve can be determined by its intersection numbers with reference curves. psychiatry liaison