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Sage torsion points of jacobian

WebOct 22, 2012 · He then applied it to the Jacobian variety of a cyclic quotient of a Fermat curve and showed that torsion points of certain prime order lay outside of the theta … WebUsing a specialization argument, I also classify torsion points on a generic superelliptic curve, extending Theorem 7.1 of Poonen–Stoll [57] to the hyperelliptic case. In order to …

Torsion points on Jacobian varieties via Anderson

http://sporadic.stanford.edu/reference/arithmetic_curves/sage/schemes/hyperelliptic_curves/jacobian_generic.html WebSep 1, 2010 · (2) As the points of a hyperelliptic curve have no structure, it is useful to examine the Jacobian variety of a curve (see [3]). Let J 1 be the Jacobian of C 1 , C (d) the quadratic twist of C 1 by d and J (d) the 1 1 Jacobian of C (d) 1 . 1966 F. Najman / Journal of NumberTheory 130 (2010) 1964–1968 Lemma 3. J 1 (Q(i)) similarequal Z 19 . Proof. nike air jordan 1 low off white https://pdafmv.com

Simple genus-2 Jacobians with rational points of high order

WebJul 9, 2014 · Also, we find the genus-3 curve 15625(X^4 + Y^4 + Z^4) - 96914(X^2 Y^2 + X^2 Z^2 + Y^2 Z^2) = 0, whose Jacobian has 864 rational torsion points. This paper has … Webproperty on the point counting algorithm are also dis-cussed in this paper. In this paper, we assume that an operation of univari-ate polynomials of degree n over Fq takes O(n1+o(1)) operations in Fq. 2 Torsion points and Frobenius map Let J be the Jacobian of a genus 2 hyperelliptic curve over a finite field Fq of odd characteristic and χ ... WebAs an application, we get a stronger result on the intersection of the theta divisor and torsion points on the Jacobian variety for more general curves. New examples are discussed as … nike air jordan 1 low mystic navy

Complete classification of torsion of elliptic curves over quadratic ...

Category:Another approach to pairing computation in Edwards coordinates

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Sage torsion points of jacobian

Introduction g k

Webpoints is 1) on the Edwards curve and on the Weierstrass form in Jacobian coordinates. We briefly remind the reader that a point (X,Y,Z) in Jacobian coordinates corresponds to the affine point (x,y) with x= X/Z2 and y= Y/Z3. We denote by M the cost of a field multiplication and by S the cost of a field squaring. WebOr more fully you'd call it the Jacobian Matrix. And one way to think about it is that it carries all of the partial differential information right. It's taking into account both of these components of the output and both possible inputs. And giving you a kind of a grid of what all the partial derivatives are.

Sage torsion points of jacobian

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WebSign In Help ... WebFor example, the rational points on a certain elliptic surface over P1 of positive rank parameterize a family of genus-2 curves over Q whose Jacobians each have 128 rational …

Webclass sage.schemes.hyperelliptic_curves.jacobian_generic. ... Set of rational points of Hyperelliptic Curve over Number Field in t with defining polynomial x^2 - 2 defined by v^2 + u*v = u^5 - u + 1 sage: P = C ... Moreover the following relation holds in … WebWe produce new explicit examples of genus-2 curves over the rational numbers whose Jacobian varieties have rational torsion points of large order. In particular, we produce a family of genus-2 curv...

WebThis representing object is the Jacobian of C. Remark 1.16 . Since P1 k has genus 0 its Jacobian should be zero, which is re ected in the isomorphism deg : Pic (P1 k)!˘ Z . Moreover, for an elliptic curve E, the Riemann Roch argument shows that Eis its own Jacobian. Remark 1.17 . Let Cbe a nice curve of genus 2 with a k-point O. Then the Riemann WebApr 21, 2024 · Generalization of torsion points on Jacobian of genus 2 over finite fields (with respect to the theta divisor) Ask Question Asked 1 year, 9 months ago. ... Like "Theta n …

WebWe produce new explicit examples of genus-2 curves over the rational numbers whose Jacobian varieties have rational torsion points of large order. In particular, we produce a …

nsw disability and ageing commissionhttp://fe.math.kobe-u.ac.jp/icms2010-dvd/SAGE/www.sagemath.org/doc/reference/sage/schemes/hyperelliptic_curves/jacobian_morphism.html nsw dine and discover locationsWebThe Jacobian of a genus-one curve can be defined as the set of line bundles on the curve, and is isomorphic to the original genus-one curve. It is also an elliptic curve with the trivial … nike air jordan 1 low white pollenWebdenoted 1 to embed X0(N) into its Jacobian i: X0(N),!J0(N). That is, a point P 2 X0(N) maps to the class of the divisor [P] ¡ [1]. In the following, we will suppress the embedding i from … nike air jordan 1 low og mystic navyWebThe difference between this point and either of the Weierstrass points is a torsion divisor of order 40, the highest known (as of 6/2001) for a simple genus-2 Jacobian. The rational … nsw dining vouchers participating outletsWebAug 12, 2024 · The main ingredient is a method to torsion points on a Jacobian in the framework of Makdisi's algorithms to compute rho, given the characteristic polynomial of … nsw dine and discover vouchers applyWebNov 6, 2024 · But it also should not be very hard to come up with examples of, say, curves of genus 2 over $\mathbb Q$ whose Jacobian has positive rank (and non-trivial torsion), but … nike air jordan 1 low red black