2024 Curves of genus 2 with split jacobian

Curves of genus 2 with split jacobian

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August undefined, 2024

WebConstructing Pairing-Friendly Genus 2 Curves with Split Jacobian 3 eties. In order to obtain pairing-friendly ordinary abelian surfaces, which generically have ˆ-value around … WebApr 23, 2009 · Curves of genus 2 have an associated abelian surface, their jacobian. One can classify genus 2 curves according to special properties of their jacobians. For instance, a jacobian can be split: isogenous to a product of elliptic curves. There are several ways in which jacobians can be split. In this talk we will give a precise description of one ...

The Arithmetic of Genus Two Curves with (4,4)-Split Jacobians …

WebDec 5, 2012 · Yuri Zarhin. 4,990 19 30. Add a comment. 4. Every curve of genus 2 has an equation of the form Y 2 Z 4 = f 0 X 6 + f 1 X 5 Z + ⋯ + f 6 Z 6. ] Flynn (1990) has found … Webto have a split Jacobian for some curves Cin positive characteristic (see e.g. discussion in [2]). In particular, one can have a Jacobian of the form J(C) = E 1 E 2;the sum of two … itunes for windows setup

DESCENT VIA -ISOGENY ON JACOBIANS OF GENUS CURVES

WebJul 25, 2008 · T. Shaska. Genus 2 curves with (3; 3)-split Jacobian and large automorphism group. In Algorithmic number theory (Sydney, 2002), volume 2369 of … WebLARGE TORSION SUBGROUPS OF SPLIT JACOBIANS OF CURVES OF GENUS TWO OR THREE EVERETT W. HOWE, FRANCK LEPREVOST, AND BJORN POONEN´ … WebNov 20, 2024 · As an application, two explicit examples of elliptic curves whose order are respectively 2 times a 149-bit prime and 2 times a 256-bit prime vulnerable to the attack … itunes for windows support site

Genus two curves covering elliptic curves: a computational approach

arXiv:1209.1239v1 [math.AG] 6 Sep 2012

WebIn genus $2$, Calta and McMullen independently discovered an infinite family of algebraically primitive Teichmüller curves. However, in higher genus, such curves seem to be much rarer. We will discuss a result that shows that the regular $14$-gon yields the unique algebraically primitive Teichmüller curve in genus $3$ of a particular ... Webgenus 2 curves, where previously only Richelot isogenies with kernels that are pointwise deﬁned over the base ﬁeld were considered. Our main tool is a Galois theoretic characterization of genus 2 curves admitting multiple Richelot isogenies. 1 Introduction Let k be a ﬁeld and letC be a curve of genus 2 over k. Let J = Jac(C) be its Jacobian. itunes for windows slowWebApr 23, 2009 · Curves of genus 2 have an associated abelian surface, their jacobian. One can classify genus 2 curves according to special properties of their jacobians. For … itunes for windows keyboard shortcuts

"Webto have a split Jacobian for some curves Cin positive characteristic (see e.g. discussion in [2]). In particular, one can have a Jacobian of the form J(C) = E 1 E 2;the sum of two elliptic curves. One has an isogeny: E 1 E 2!E 1 E 2 de ned as an identity on E 1;and as a power of Frobenius on E 2: We must note that in this example we do not know ... " - Curves of genus 2 with split jacobian

Curves of genus 2 with split jacobian

Weekly Seminars Department of Mathematics

WebJun 14, 2013 · It follows that the genus two curves whose Jacobian decomposes in this way are precisely those which admit map to an elliptic curve. ... So this is a construction … WebSep 6, 2016 · (4,4)-split Jacobians of curves of genus 2 - YouTube Curves of genus 2 have an associated abelian surface, their jacobian. One can classify genus 2 curves according to special...

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WebJan 1, 2002 · Let C be a genus 2 curve defined over k, char (k)=0. If C has a (3,3)-split Jacobian then we show that the automorphism group Aut (C) is isomorphic to one of the … WebIn this survey we study the genus 2 curves with (n,n)-split Jacobian for small n. While such curves have been studied by many authors, our approach is simply computational. Some of the results have appeared in previous articles of the author. Curves of genus 2 with elliptic subcovers go back to Legendre and Jacobi. Le-gendre, in his Th´eorie ...

Web2. Five-torsion on genus two Jacobians Let kbe a eld of characteristic di erent from 2;3 and let Cbe a smooth projective curve of genus 2 over kgiven by an a ne model C: y2 = F(x); where F(x) 2k[x] is of degree 5 or 6 (this only mildly restricts the admissible Cif kis a nite eld of 5 elements). Let Jbe the Jacobian of C. WebLet kbe a ﬁeld and let Cbe a curve of genus 2 over k. Let J= Jac(C) be its Jacobian. The abelian variety is called decomposable over kif J is isogenous over kto a product of elliptic curves E1 × E2. A genus 2 curve has a decomposable Jacobian if and only if there is a cover φ1: C→ E1 to an elliptic curve E′. If we take φ

WebMar 17, 2024 · Curves of Genus 2 with Split Jacobian Article May 1988 Robert M. Kuhn View Show abstract Prym varieties and fourfold covers. II: The dihedral case Article Jan 2006 Sevin Recillas Rubí E.... WebSep 14, 2012 · A genus 2 curve has an elliptic subcover if there exists a degree maximal covering to an elliptic curve . Degree elliptic subcovers occur in pairs . The Jacobian of …

WebJan 1, 2002 · There are exactly six ℂ-isomorphism classes of genus two curves \mathcal {C} with Aut ( \mathcal {C} ) isomorphic to D 8 (resp., D 12) and with (3, 3)-split …

WebWe study degree 2 and 4 elliptic subcovers of hyperelliptic curves of genus 3 defined over ℂ. The family of genus 3 hyperelliptic curves which have a degree 2 cover to an elliptic curve E and degree 4 covers to elliptic curves E 1 and E 2 is a 2-dimensional subvariety of the hyperelliptic moduli ${\mathcal H}_3$.We determine this subvariety explicitly. netflix movies about writersWebJun 20, 2008 · In this article, we give a new proof of the existence of curves of genus 5 and 17 with split Jacobian by constructing explicit two families of such curves over number fields. Key Words: Algebraic curves Splitting of Jacobian variables. 2000 Mathematics Subject Classification: 14H40 14Q05. netflix movies about orthodox jewsWebAbstract. We decompose the Jacobian variety of hyperelliptic curves up to genus 20, de ned over an algebraically closed eld of characteristic zero, with reduced automorphism group A 4, S 4, or A 5: Among these curves is a genus 4 curve with Jacobian variety isogenous to E2 1 2E 2 and a genus 5 curve with Jacobian variety isogenous to E5, for … netflix movies about warWebthe fact that we construct the curve Cin the theorem as a genus-2 curve with split Jacobian J ˘E 1 E 2, and this requires the construction of auxiliary elliptic curves E 1 and E 2 of given orders. Such elliptic curves can be constructed by the method of [3] discussed in x2. The Jacobian Jof Cis then obtained by gluing E 1 and E netflix movies about ww2WebGenus 2 curves with given split Jacobian Jasper Scholten [email protected] November 22, 2024 Abstract Given 2 Elliptic Curves E 1 and E 2, we use some theory of elliptic Kummer surfaces to construct a hyperelliptic curve with Jacobian isogenous to E 1 E 2. We require the 2-torsion of E 1 and E 2 to be de ned over the eld we are working ... itunes for windows vistaWebEnter the email address you signed up with and we'll email you a reset link. itunes fotos synchronisierenWebDec 5, 2012 · Yuri Zarhin. 4,990 19 30. Add a comment. 4. Every curve of genus 2 has an equation of the form Y 2 Z 4 = f 0 X 6 + f 1 X 5 Z + ⋯ + f 6 Z 6. ] Flynn (1990) has found the equations of the Jacobian variety of such a curve in characteristic ≠ 2, 3, 5 --- they form a set 72 homogeneous equations of degree 2 in 16 variables (they take 6 pages to ... itunes for windows 開けない