A new record for the canonical height on an elliptic curve over .

Jain, Sonal

Displaying similar documents to “A new record for the canonical height on an elliptic curve over $ℂ (t)$ .”

Spectral curves of operators with elliptic coefficients.

Eilbeck, J.Chris, Enolski, Victor Z., Previato, Emma (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Quasi-modular forms attached to elliptic curves, I

Hossein Movasati (2012)

Annales mathématiques Blaise Pascal

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In the present text we give a geometric interpretation of quasi-modular forms using moduli of elliptic curves with marked elements in their de Rham cohomologies. In this way differential equations of modular and quasi-modular forms are interpreted as vector fields on such moduli spaces and they can be calculated from the Gauss-Manin connection of the corresponding universal family of elliptic curves. For the full modular group such a differential equation is calculated and it turns out...

Weierstrass gaps and curves on a scroll.

Carvalho, Cícero (2002)

Beiträge zur Algebra und Geometrie

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Torsion and Tamagawa numbers

Dino Lorenzini (2011)

Annales de l’institut Fourier

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Let $K$ be a number field, and let $A / K$ be an abelian variety. Let $c$ denote the product of the Tamagawa numbers of $A / K$ , and let $A {(K)}_{tors}$ denote the finite torsion subgroup of $A (K)$ . The quotient ${c / | A (K)}_{tors} |$ is a factor appearing in the leading term of the $L$ -function of $A / K$ in the conjecture of Birch and Swinnerton-Dyer. We investigate in this article possible cancellations in this ratio. Precise results are obtained for elliptic curves over $ℚ$ or quadratic extensions $K / ℚ$ , and for abelian surfaces $A / ℚ$ . The smallest possible...

Regulators of rank one quadratic twists

Christophe Delaunay, Xavier-François Roblot (2008)

Journal de Théorie des Nombres de Bordeaux

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We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists of a fixed elliptic curve. In particular, we formulate some conjectures on the average size of these regulators. We also describe an efficient algorithm to compute explicitly some of the invariants of a rank one quadratic twist of an elliptic curve (regulator, order of the Tate-Shafarevich group, etc.) and we discuss the numerical data that we obtain and compare it with our predictions. ...

Operations of Points on Elliptic Curve in Projective Coordinates

Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama (2012)

Formalized Mathematics

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In this article, we formalize operations of points on an elliptic curve over GF(p). Elliptic curve cryptography [7], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security. We prove that the two operations of points: compellProjCo and addellProjCo are unary and binary operations of a point over the elliptic curve.

Siegel’s theorem and the Shafarevich conjecture

Aaron Levin (2012)

Journal de Théorie des Nombres de Bordeaux

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It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field $k$ and any finite set of places $S$ of $k$ , one can effectively compute the set of isomorphism classes of hyperelliptic curves over $k$ with good reduction outside $S$ . We show here that an extension of this result to an effective Shafarevich conjecture for of hyperelliptic curves of genus $g$ would imply an effective version of Siegel’s theorem for integral points...

On torsion points on an elliptic curves via division polynomials.

Ulas, Maciej (2005)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Displaying similar documents to “A new record for the canonical height on an elliptic curve over ℂ ( t ) .”

Displaying similar documents to “A new record for the canonical height on an elliptic curve over $ℂ (t)$ .”