Curves of genus 2 with split jacobian

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August undefined, 2024

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

Equation for simple Jacobian of a genus two curve - MathOverflow

WebAbstract. 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 … 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 ... bissell cleanview pet slim cordless vacuum

Relationships Between Hyperelliptic Functions of Genus 2 and

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 … 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... 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 … bissell cleanview proheat 53u6e belt

DESCENT VIA -ISOGENY ON JACOBIANS OF GENUS CURVES

Genus 2 Curves with (3 3)-Split Jacobian and Large ... - Springer

WebThe study of genus 2 curves with split Jacobian has a long history which arguably started with the task of reducing hyperelliptic integrals of genus 2 of the ﬁrst kind to sums of elliptic integrals. Here a substitution of variables gives rise to a genus 2 cover of an elliptic curve. The study for degree 2 dates 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 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 ... darryl\u0027s greensboro ncWebgenus 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. bissell cleanview plus rewind upright vacuum

"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 ... " - Curves of genus 2 with split jacobian

Curves of genus 2 with split jacobian

LARGE TORSION SUBGROUPS OF SPLIT JACOBIANS …

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 ... 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 …

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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 … 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.

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. 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 …

WebJun 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. 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 …

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 ... darryl\u0027s gun shop newmanstown paWebJan 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 … darryl\u0027s lock and key medicine hatWebMar 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.... darryl\u0027s gun shop - newmanstownWebJul 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 … darryl\u0027s lock and key in greenville msWebJun 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 … darryl\u0027s taxidermy grand junctionWebthe 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 darryl\u0027s gun shop newmanstownWebNov 20, 2024 · Genus 2 curves with given split Jacobian Jasper Scholten [email protected] November 20, 2024 Abstract Given 2 Elliptic Curves E1and E2, we use some theory of elliptic Kummer... darryl wagstaff funerals maryborough