Curves of genus 2 with split jacobian

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August undefined, 2024

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 … WebLARGE TORSION SUBGROUPS OF SPLIT JACOBIANS OF CURVES OF GENUS TWO OR THREE EVERETT W. HOWE, FRANCK LEPREVOST, AND BJORN POONEN´ …

Consider the following: Let X be a curve of genus 2, …

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 … 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. hugs eating

On Curves with Split Jacobians - Taylor & Francis

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 … WebUsing genus 2 curves with simple but not absolutely simple Jacobians one can obtain pairing-based cryptosystems more efficient than for a generic genus 2 curve. We describe a new framework to construct pairing-friendly abelian surfaces, which are simple but not absolutely simple. 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 hugs emoticon

Genus 2 curves with given split Jacobian - IACR

Equation for simple Jacobian of a genus two curve

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 … 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... holiday inn northwood santryWebJun 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. hugs donuts houston

"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. " - Curves of genus 2 with split jacobian

Curves of genus 2 with split jacobian

Equation for simple Jacobian of a genus two curve

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.... WebGenus 2 Curves with (3,3)-Split Jacobian and Large Automorphism Group Tony Shaska UniversityofCaliforniaatIrvine,Irvine,CA92697. [email protected] …

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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 ... Webthe 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

WebReferences. Athorne C., Eilbeck J.C., Enolskii V.Z., A ${\rm SL}(2)$ covariant theory of genus 2 hyperelliptic functions, Math. Proc. Cambridge Philos. Soc. 136 (2004 ... 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 ...

WebWe study the singular locus on the space of genus 2 curves with a (n;n)-split Jacobian. Such curves have been of much interest lately because of their use in many theoretical and applicative situations. The rst part of the paper is based on several papers on the topic of genus two curves with split Jacobians; see [1,3{9,11{14,16{21] among others. 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.

WebApr 17, 2024 · We will talk about the Ceresa class, which is the image under a cycle class map of a canonical homologically trivial algebraic cycle associated to a curve in its …

WebApr 1, 2024 · It turns out that only one (hyperelliptic) curve in genus 3 and two curves in genus 4 have Jacobians not of CM type. The main new results of the present paper are contained in Sections 4, 5 and 7. hug seat cushionWebConstructing 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 … holiday inn norwalk ctWebGenus 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 … holiday inn norwalk ohioWebSplit jacobian curves of genus 2 have also been used to exhibit nonisomorphic curves with the same jacobian; vide [3, 4]. The approach in these papers is through the algebraic geometry of abelian varieties, and the constructions are therefore far from explicit. … holiday inn northwest waco txWebJun 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 … holiday inn northwest urbandale iowaWebEnter the email address you signed up with and we'll email you a reset link. hug service facturationWebSep 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 … hug service angiologie